1 


: 


•-, 


. 


THE  PRINCIPLES  OF 
DYNAMO  ELECTRIC  MACHINERY 


McGraw-Hill  BookCompany 

PurfGsfiers  of£oo£§for 

Electrical  World         The  Engineering  and  Mining  Journal 
En5ineering  Record  Engineering  News 

Railway  Age  Gazette  American  Machinist 

Signal  Engineer  American  Engineer 

Electric  Railway  Journal  Coal  Age 

Metallurgical  and  Chemical  Engineering  Power 


THE  PRINCIPLES  OF 

DYNAMO  ELECTRIC 
MACHINERY' 


BY 


BENJAMIN  F.  BAILEY,  B.  S.,  PH.  D. 

PROFESSOR   OF   ELECTRICAL   ENGINEERING 
TJNIVEB8ITY   OF   MICHIGAN 


FIRST  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC. 
239  WEST  39TH  STREET,  NEW  YORK 

6  BOUVERIE  STREET,  LONDON,  E.  C. 

1915 


COPYRIGHT,  1915,  BY  THE 
MCGRAW-HILL  BOOK  COMPANY,  INC. 


THE     M    \    i-r.i       PXK88     YOHIC 


PREFACE 

The  underlying  purpose  which  the  writer  has  had  in  mind 
throughout  the  preparation  of  this  book  is  to  present  a  clear 
physical  conception  of  the  phenomena  which  take  place  in 
electrical  machinery.  He  has  made  but  sparing  use  of  mathe- 
matical demonstration,  not  because  he  does  not  believe  in  the 
value  of  mathematics  to  the  engineer,  but  because  he  is  firmly 
convinced  that  a  clear  physical  idea  of  the  actions  which  take 
place  should  be  obtained  before  an  attempt  is  made  to  apply 
mathematical  analysis.  This  method  of  studying  the  subject 
is  by  no'  means  easy  either  for  the  student  or  for  the  teacher. 
It  is  not  easy  for  the  student  because  it  requires  the  development 
of  his  ability  to  think  clearly  and  to  express  his  ideas  in  logical 
language.  It  is  not  easy  for  the  teacher,  because  while  it  is  a 
simple  matter  to  glance  through  a  mathematical  demonstration 
and  pick  out  the  errors,  real  teaching  ability  is  required  to  guide 
the  student  so  that  he  will  form  correct  habits  of  thought,  and  to 
make  some  effort  to  determine  whether  or  not  he  has  a  real  under- 
standing of  the  subject.  Thus  it  is  very  easy  to  tell  the  student 
that  two  harmonic  motions  at  90  degrees  in  both  time  and  space, 
combine  to  form  a  rotary  motion.  The  student  sees  no  objection 
to  the  statement,  accepts  it  as  true  and  very  readily  learns  to 
repeat  it.  It  is  doubtful,  however,  whether  he  has  materially 
increased  his  reasoning  power.  In  fact,  in  the  writer's  opinion, 
he  has  decreased  it  and  instead  has  taken  a  step  toward  acquiring 
the  bad  habit  of  accepting  a  statement  as  true  "because the  book 
says  so."  If,  on  the  other  hand,  he  has  carefully  studied  the  way 
in  which  the  currents  rise  and  fall  in  the  conductors  of  a  polyphase 
induction  motor,  and  has  mastered  the  way  in  which  the  current 
sheet  and  consequently  the  flux  revolve  around  the  stator,  he 
has  made  a  start  toward  acquiring  a  real  power  of  analysis.  This 
will  stand  him  in  good  stead  when  in  later  years  he  is  confronted 
with  problems  whose  answer  is  not  "in  the  back  of  the  book." 

It  is  believed  that  the  material  presented  is  sufficient  to  satisfy 
the  needs  of  students  who  do  not  intend  to  follow  electrical 


325816 


vi  PREFACE 

engineering  as  a  profession.  It  is  also  thought  that  it  is  well 
adapted  as  a  first  text  in  electrical  engineering  for  students  who 
do  expect  to  go  further  with  the  subject.  In  this  case,  it  should 
be  followed  by  a  text  going  into  the  mathematical  relations.  The 
student  who  has  mastered  the  contents  of  this  book  should  be 
well  prepared  to  take  such  a  course  with  profit  and  understanding. 

As  an  illustration  of  what  may  happen  if  the  mathematics  of 
electrical  engineering  is  taught  before  a  physical  conception  of  the 
actions  which  take  place  has  been  acquired,  the  writer  may  cite 
the  case  of  a  student  who  recently  came  to  him  for  an  examina- 
tion. The  young  man  reproduced  very  well  several  pages  of 
mathematical  demonstrations  relating  to  transformers,  and  all 
would  have  been  well  had  not  a  chance  question  revealed  the 
fact  that  he  believed  all  the  time  that  the  function  of  the  trans- 
former was  to  step  up  or  step  down  the  voltage  of  a  continuous 
current  circuit.  This  is  by  no  means  an  isolated  case.  There  are 
many  others  nearly  as  bad. 

The  scope  of  the  book  is  such  as  to  teach  the  student  two  things 
about  each  machine  studied:  first,  what  the  machine  will  do; 
second,  why  it  does  it.  No  attempt  is  made  to  take  up  questions 
relating  to  the  design  of  electrical  machinery. 

The  writer  desires  to  acknowledge  with  gratitude  the  assistance 
given  him  by  his  associates  on  the  faculty  of  the  University  of 
Michigan  in  the  preparation  of  this  work. 

B.  F.  B. 

ANN  ARBOR,  MICH., 
Oct.,  1915. 


CONTENTS 

PAGE 

PREFACE    v 

CHAPTER  I 

GENERAL  PRINCIPLES 

1.  Effects  of  Electricity 1 

2.  Ohm's  Law 2 

3.  Resistance 2 

4.  Resistors  in  Series  and  in  Parallel .  3 

5.  The  Wire  Table 4 

6.  Magnetism 5 

7.  Strength  of  Field 6 

8.  Permeability 6 

9.  Generation  of  Electromotive  Force 6 

10.  Force  on  a  Conductor  in  a  Magnetic  Field 7 

11.  Work '............  8 

12.  Solenoids 8 

13.  Force  in  a  Solerioid    .    .    . 9 

14.  Magnetomotive  Force 10 

15.  Magnetic  Circuit 10 

16.  Variation  of  Permeability 11 

17.  Magnetization  Curves 12 

CHAPTER  II 
ELECTRIC  MOTORS 

18.  Elementary  Form  of  Electric  Motor 15 

19.  The  Armature 16 

20.  The  Field  Magnet 18 

21.  Operation  as  a  Motor 18 

22.  The  Commutator 19 

23.  Action  of  the  Forces  in  a  Motor      20 

24.  Force  Acting  upon  a  Current  in  a  Magnetic  Field 20 

25.  Multipolar  Machines 21 

26.  Construction  of  the  Drum-wound  Armature 21 

27.  Connections  of  a  Lap-wound  or  Parallel-wound  Armature ....  23 

28.  The  Wave  Winding    . 25 

vii 


Vlll  CONTENTS 

PAGE 

29.  Number  of  Coils  in  Wave-wound  Armature      27 

30.  Construction  of  Small  Motor 27 

CHAPTER  III 
GENERAL  PRINCIPLES  OF  DYNAMOS  AND  MOTORS 

31.  Classification  of  Dynamos  and  Motors 28 

32.  General  Principles 29 

33.  Commutators 31 

34.  Action  as  a  Generator 32 

35.  Back  E.M.F 33 

36.  Calculation  of  E.M.F 34 

37.  Methods  of  Field  Excitation 35 

38.  The  Shunt-wound  Machine 36 

39.  The  Series-wound  Machine 37 

40.  The  Compound-wound  Machine      37 

41.  Magnetic  Effect  of  the  Armature 37 

42.  Armature  Reaction 38 

CHAPTER  IV 
SYSTEMS  OF  DISTRIBUTION 

43.  The  Constant  Current  System 41 

44.  The  Constant  Potential  System 43 

45.  Regulation  of  Generators 45 

46.  Regulation  for  Constant  Potential 45 

47.  The  Shunt-wound  Generator 47 

48.  The  Series-wound  Generator 49 

49.  The  Compound-wound  Generator .    .  51 

50.  Method  of  Testing  Regulation 53 

51.  Parallel  Operation  of  Generators 54 

52.  Shunt  Generators  in  Parallel 55 

53.  Compound-wound  Generators  in  Parallel 56 

54.  Effect  of  Voltage  upon  the  Amount  of  Copper  Required    ....  58 

55.  The  Three-wire  System 59 

CHAPTER  V 
CHARACTERISTICS  OF  MOTORS 

56.  Characteristics  of  Motors 61 

57.  Operation  of  same  Machine  either  as  a  Generator  or  as  a  Motor.  61 

58.  The  Fundamental  Equation  of  the  Direct-current  Motor  ....  63 

59.  Speed  Torque  Curve  of  Shunt  Motor 64 

60.  The  Series-wound  Motor 65 

61.  The  Compound-wound  Motor 67 

62.  The  Differential  Compound  Motor 68 


CONTENTS  ix 

PAGE 

63.  The  Choice  of  Motors  for  any  Particular  Service 69 

64.  The  Series  Motor    .    . 69 

65.  The  Compound-wound  Motor 70 

66.  Direction  of  Rotation  of  Motors  and  Generators 71 

CHAPTER  VI 
ACCESSORY  APPARATUS 

67.  Starting  Rheostats,  Series  Motors 74 

68.  Starting  Rheostats  for  Shunt  Motors 74 

69.  The  No-voltage  Release 76 

70.  Protective  Apparatus 76 

71.  Circuit  Breakers 77 

CHAPTER  VII 
RATING  OF  MACHINES 

72.  Influence  of  Speed      79 

73.  Heating 80 

74.  Efficiency 81 

75.  Sparking 82 

76.  Resistance  Commutation 83 

77.  Effect  of  Rocking  the  Brushes 85 

78.  Commutating  Poles 86 

CHAPTER  VIII 

EFFICIENCIES  AND  LOSSES 

79.  Efficiency 88 

80.  Methods  of  Determining  Efficiency 88 

81.  The  Stray  Power  Method 89 

82.  Losses  in  Direct-current  Machines 89 

83.  Stray  Power  Loss 90 

84.  Shunt  Field  Loss 91 

85.  Armature  Copper  Loss 92 

86.  Calculation  of  Efficiency  of  a  Shunt  Motor 93 

87.  Performance  Curves 95 

88.  Efficiency  of  a  Generator 96 

89.  Change  of  Efficiency  with  Speed 96 

CHAPTER  IX 

DIRECT-CURRENT  MEASURING  INSTRUMENTS 


90.  Voltmeter  and  Ammeters      .... 

91.  The  D'Arsonval  Type  of  Instrument 


X  CONTENTS 

PAGE 

92.  The  Voltmeter 100 

93.  The  Plunger  Type  of  Instrument 100 

94.  Measurement  of  Power 101 

95.  Measurement  of  Work 101 

CHAPTER  X 
ADJUSTABLE  SPEED  MOTORS 

96.  Adjustable  Speed  Motors      -.   ,    .  104 

97.  Shunt  Field  Control 104 

98.  Use  of  Commutating  Poles 106 

99.  Methods  of  Changing  the  Magnetic  Circuit      106 

100.  Speed  Variation  by  Means  of  Resistance  in  the  Armature  Circuit.  107 

101.  Motors  with  Two  Commutators 109 

102.  The  Multi-voltage  System 110 

103.  The  Ward-Leonard  System Ill 

104.  Rolling  Mills   .    . 112 

105.  Propulsion  of  Ships 113 

106.  Operation  of  Gas-electric  Cars 113 

CHAPTER  XI 
ALTERNATING  CURRENTS 

107.  General  Principles 116 

108.  Definition  of  an  Alternating  Current 117 

109.  Wave  Shape 117 

110.  Frequency 119 

111.  Construction  of  Sine  Curves 120 

112.  Methods  of  Treating  Alternating-current  Waves 121 

113.  Analytical  Method 121 

114.  Vector  Method 121 

115.  Phase  Difference 122 

116.  Addition  of  Two  Waves 122 

117.  Vector  Addition 123 

118.  Effective  Values  of  Current  and  E.  M.  F 124 

CHAPTER  XII 
INDUCTANCE  AND  CAPACITANCE 

119.  Alternating-  and  Direct-Currents  Compared 126 

120.  E.M.F.     Due  to  Inductance 126 

121.  Coefficient  of  Inductance 127 

122.  Mechanical  Analogy 128 

123.  Starting  a  Mass  or  a  Current 129 

124.  Field  Discharge  Switch 132 

125.  Resistance  and  Inductance 133 


CONTENTS  xi 

PAGE 

126.  Mechanical  Analogy 133 

127.  Resistance  without  Inductance  or  Capacitance 134 

128.  Inductance  without  Resistance -.    .  135 

129.  Power  in  Inductive  Circuit 136 

130.  Application  to  Steam  Engine 137 

131.  Circuits  Having  Both  Resistance  and  Inductance 138 

132.  Vector  Representation 138 

133.  Calculation  of  Power .138 

134.  Mathematical  Treatment      140 

135.  Power 141 

136.  Power  Factor 142 

137.  The  Condenser 142 

138.  Circuit  Containing  a  Condenser  Only 145 

139.  Capacitance  of  Transmission  Lines 146 

140.  Circuits  Containing  Resistance,  Inductance  and  Capacitance    .    .  147 

141.  Vector  Representation 149 

142.  Mathematical  Treatment      150 

143.  Resistance,  Reactance  and  Impedance 152 

144.  Resonance 152 

145.  Oscillatory  Discharges 154 

CHAPTER  XIII 

ALTERNATING-CURRENT  MEASURING  INSTRUMENTS 

146.  Action  of  Direct-current  Instruments  on  Alternating  Current  Cir- 
cuits   ' 158 

147.  The  Electrodynamometer  Type 158 

148.  The  Wattmeter 159 

149.  Hot  Wire  Instruments 160 

150.  The  Spark  Gap 162 

151.  The  Electrostatic  Voltmeter 162 

152.  The  Oscillograph 162 

CHAPTER  XIV 
SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 

153.  Alternating-current  Generators 164 

154.  The  Two-phase  Generator 166 

155.  Electromotive  Force  of  an  Alternator 168 

156.  Method  of  Connecting  Load 168 

157.  Three-phase  Systems 170 

158.  Advantages  of  Three-phase  over  Single  phase  .    .    . 171 

159.  Three-phase  Connections 173 

160.  Voltage  and  Current  Relations 174 

161.  Power  in  Balanced  Three-phase  Circuits 175 

162.  Substitution    of    a    Three-phase    Alternator   for    a    Single-phase 
Machine    ....  • 175 


xii  CONTENTS 

PAGE 

163.  Rotating  Magnetic  Field  in  the  Armature  of  the  Alternator  ...  176 

164.  Action  with  Single-phase  Alternating  Current 176 

165.  Action  with  Two-phase  Alternating  Current 176 

166.  Action  with  a  Three-phase  Current 177 

167.  The  Synchronous  Motor 177 

168.  Measurement  of  Power  in  Polyphase  Circuits 178 

169.  Measurement  of  Power  in  Three-phase  Circuits 179 

170.  The  Two-wattmeter  Method 180 

171.  Polyphase  Wattmeters 181 

172.  Power  Factor  of  Unbalanced  Polyphase  Circuits      .......  182 

173.  Line  Regulation 182 

174.  Regulation  of  100  Per  Cent.  Power  Factor 182 

175.  Regulation  with  Lagging  Current 183 

176.  Regulation  with  Leading  Current 183 

CHAPTER  XV 
THE  TRANSFORMER 

177.  Transformation  of  Continuous  Current 185 

178.  General  Construction  of  Transformer 185 

179.  Elementary  Theory 186 

180.  Core  Loss 187 

181.  Vector  Diagram  of  Unloaded  Transformer 188 

182.  Transformers  under  Load 190 

183.  Leakage  Flux 192 

184.  Regulation 193 

185.  Constant-current  Transformers - 193 

186.  Instrument  Transformers 195 

187.  Types  of  Transformers 197 

188.  Cooling  of  Transformers 198 

189.  Losses  and  Efficiency  of  Transformers 200 

190.  Connection  of  Transformers — Single  Phase 201 

191.  Two-phase  Connections 202 

192.  Three-phase  Connections 202 

193.  Three-phase  Transformers 205 

194.  The  Open-delta  Connection      205 

195.  Transformation  of  the  Number  of  Phases      206 

CHAPTER  XVI 
SYNCHRONOUS  GENERATORS  AND  MOTORS 

196.  General  Construction 208 

197.  Action  as  a  Generator 211 

198.  Space  Curve  of  E.M.F 212 

199.  Space  Curve  of  Flux  and  Current 212 

200.  Torque  in  a  Synchronous  Machine 213 


CONTENTS  xiii 

PAGE 

201.  Effect  of  Power  Factor  on  Torque 214 

202.  The  Case  of  Zero  Power  Factor 215 

203.  Influence  of  the  Number  of  Phases. 216 

204.  Synchronous  Machines  in  Parallel 218 

205.  Relations  of  E.M.F.  and  Current 219 

206.  Effect  of  Change  of  Field  Current 221 

207.  Effect  of  Regulation  of  Prime  Mover 222 

208.  Treatment  by  Means  of  Vectors      223 

209.  The  Synchronous  Condenser 224 

210.  Operation  with  Distorted  Waves 225 

211.  Hunting 226 

212.  Prevention  of  Hunting 227 

213.  Damping  Grids 228 

214.  The  Synchronous  Motor 229 

215.  Methods  of  Starting 229 

216.  The  Synchroscope 230 

217.  Direct  Starting  of  the  Synchronous  Motor 232 

218.  Combination  Methods  of  Starting 233 

219.  Armature  Reaction 234 

220.  Regulation 235 

221.  Rating  of  Synchronous  Machine 236 

222.  Regulation  in  Large  Machines 237 

223.  Effect  of  Good  Regulation  in  the  Synchronous  Motor 238 

224.  Synchronous  Condensers 238 

CHAPTER  XVII 

THE  ROTARY  CONVERTER  OR  SYNCHRONOUS  CONVERTER 

225.  General  Description 241 

226.  General  Operation 241 

227.  Field  Winding 242 

228.  Voltage  Relations 242 

229.  Starting ' 243 

230.  Reversed  Polarity  at  Start 244 

231.  Voltage  Control 245 

232.  Use  of  Voltage  Regulators .' 247 

233.  Split-pole  Rotaries 249 

234.  Heating  of  Rotary  Converters 251 

235.  Commutation  of  Rotaries 252 

236.  Frequency 252 

237.  Connections  of  Rotaries 253 

238.  Rotary  Converters  versus  Motor-generator  Sets 256 

239.  Cost 257 

240.  Frequency 257 

241.  Efficiency 257 

242.  Regulation 257 


xiv  CONTENTS 

PAGE 

243.  The  Cascade  Converter 258 

244.  The  Mercury  Arc  Rectifier 260 

CHAPTER  XVIII 
THE  INDUCTION  MOTOR 

245.  General  Description 264 

246.  The  Stator 264 

247.  The  Rotor 264 

248.  The  Rotating  Magnet  Field .....    .  266 

249.  The  Production  of  Current  in  the  Rotor .    ....    .266 

250.  Rotor  Current -  .    .    . 267 

251.  Production  of  Torque 267 

252.  Influence  of  the  Resistance  of  the  Rotor  upon  Starting  Torque    .    .  268 

253.  The  Use  of  the  Wound  Rotor 268 

254.  Conditions  at  Normal  Speed 268 

255.  Speeds  of  Induction  Motors 269 

256.  The  Induction  Generator      270 

257.  Vector  Diagrams  of  the  Induction  Motor      271 

258.  Full-load  Diagrams 272 

259.  Diagram  Representing  the  Conditions  at  Start 273 

260.  The  Circle  Diagram 273 

261.  Starting  Devices  for  Squirrel-cage  Motors 275 

262.  The  Auto-starter 276 

263.  Resistance  Starters  for  Squirrel-cage  Motors 277 

264.  Star-delta  Starters 278 

265.  Starters  for  Motors 278 

266.  Adjustable-speed  Induction  Motors 278 

267.  Changing  the  Number  of  Poles 279 

268.  Connection  in  Cascade  or  Concatenation 279 

269.  Induction  Motors  with  Commutators 280 

270.  The  Wound-rotor  Machine  for  Adjustable  Speed  Work     .    .    .    .281 

271.  The  Single-phase  Induction  Motor 282 

272.  Rotating  Magnetic  Field  .    .    ' 282 

273.  Starting  Torque      284 

274.  Split-phase  Starters 284 

275.  Starting  as  a  Repulsion  Motor 285 

276.  Synchronous  Motors  versus  Polyphase  Induction  Motors  ....  285 

277.  Power  Factor 285 

278.  Speed  Regulation 286 

279.  Overload  Capacity 286 

280.  Hunting 286 

281.  Starting  Torque      286 

282.  Air-gap  Clearance 286 

283.  Attention  Required 287 

284.  Slow-speed  Motors 287 


CONTENTS  xv 
CHAPTER  XIX 

THE  SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR 

PAGE 

285.  Methods  of  Operating  Electric  Locomotives 289 

286.  The  Single-phase  System 290 

287.  Series-wound,  Commutator  Type,  Single-phase  Motor 290 

288.  Heating 291 

289.  Power  Factor 291 

290.  Generated  E.M.F 292 

291.  Induced  E.M.F .292 

292.  Vector  Diagram  of  Motor 293 

293.  Changes  to  Improve  Power  Factor 293 

294.  Compensating  Winding 294 

295.  Variation  of  Power  Factor  with  the  Load      295 

296.  Operation  on  Direct  Current 296 

297.  Commutation 297 

298.  Control  of  Single-phase  Motors 298 

299.  Other  Types  of  Single-phase  Commutator  Motors 300 

300.  Repulsion  Motor 301 

INDEX                                                                                                            .  303 


PRINCIPLES 

OF 

DYNAMO  ELECTRIC  MACHINERY 

CHAPTER  I 
GENERAL  PRINCIPLES 

Before  reading  this  book,  the  student  is  supposed  to  have  some 
knowledge  of  elementary  electrical  theory.  Therefore  only  a 
brief  review  of  electrical  principles  will  be  given  here. 

1.  Effects  of  Electricity. — The  ultimate  nature  of  electricity  is 
unknown  to  us.  We  are,  however,  able  to  recognize  the  presence 
of  an  electric  current  by  means  of  many  well-known  effects. 
For  example,  if  we  were  required  to  determine  whether  or  not  a 
certain  wire  were  carrying  a  current  of  electricity,  we  could  solve 
the  problem  in  many  ways.  Thus,  the  wire  would  be  somewhat 
hotter  than  the  surrounding  air,  and  if  the  current  were  strong 
enough  the  wire  might  become  red  hot  and  finally  fuse.  If  the 
wire  were  placed  in  approximately  a  north  and  south  direction, 
and  a  compass  needle  were  brought  near  the  wire,  it  would  ex- 
hibit a  tendency  to  set  itself  in  an  east  and  west  direction  across 
the  wire.  If  the  current  were  alternating,  and  the  needle  were 
light  enough  to  follow  the  alternations,  it  would  be  set  in  vibra- 
tion. If  the  wire  were  cut  and  the  ends  placed  in  a  conducting 
solution,  there  would  in  general,  if  the  current  were  direct,  be  an 
evolution  of  gases  or  products  of  the  decomposition  of  the  sub- 
stance in  solution  at  the  ends  of  the  wire.  This  result  would  also 
follow  in  many  cases  if  the  current  were  alternating.  Currents 
have  also  a  physiological  effect,  and  hence  can  be  perceived  by  the 
senses.  Thus  many  can  testify  that  a  current  can  be  felt, 
and  although  we  can  not  see  a  current  of  electricity,  it  is  easy  to 
produce  the  effect  of  flashes  of  light  by  means  of  currents  passed 
through  the  head. 

It  is  a  common  belief  that  we  know  little  or  nothing  about 
electricity,  and  that  when  its  real  nature  is  discovered  we  shall 
see  a  tremendous  advance  in  its  applications.  But  we  know  just 

1 


2 /'.  !  &®lftCli*t*ES  OF.  DYNAMO  ELECTRIC  MACHINERY 

as  little  about  the  nature  of  gravity  as  we  do  about  that  of  elec- 
tricity. This  ignorance,  however,  does  not  prevent  us  from 
making  reasonably  good  derricks,  and  it  is  doubtful  if  the  dis- 
covery of  the  exact  nature  of  gravity  would  enable  us  to  improve 
the  common  derrick  materially.  This  slight  digression  is  made 
merely  to  remove  the  impression  that  electricity  is  very  mys- 
terious and  subtle,  and  that  we  know  very  little  about 
it.  In  the  future,  undoubtedly,  we  shall  learn  many  things 
now  undreamed  of  in  regard  to  the  phenomena  of  electricity. 
There  is,  however,  no  probability  that  this  added  knowledge 
will  make  useless  any  of  the  laws  already  discovered. 

2.  Ohm's  Law. — The  simplest  and  the  most  useful  of  the  laws 
of  continuous  electricity  is  known  as  Ohm's  Law,  after  its  dis- 
coverer.    It  may  be  expressed  in  the  form 

7-£ 

R 

which  may  readily  be  changed  to  the  forms 

E  =  RI 

7?       E 
R---J 

The  equations  in  the  forms  given  apply  only  to  continuous 
currents,  that  is,  to  currents  whose  direction  and  magnitude  do 
not  vary. 

In  this  equation,  E  is  the  electromotive  force  of  the  circuit, 
and  is  generally  designated  for  the  sake  of  brevity  as  the  e.m.f., 
R  is  the  resistance  and  /  is  the  current.  The  e.m.f.  may  be 
produced  in  various  ways,  as  by  means  of  a  voltaic  cell,  by  heating 
the  junction  of  two  dissimilar  metals,  by  revolving  coils  of  wire 
in  a  magnetic  field,  and  in  other  ways.  The  e.m.f.  is  expressed 
in  volts,  the  resistance  in  ohms,  and  the  current  in  amperes. 

3.  Resistance. — The  resistance  of  a  conductor  varies  with  the 
nature  of  the  material.     It  is  directly  proportional  to  its  length, 
and  inversely  proportional  to  its  cross  section.     These  relations 
are  self-evident,  and  may  be  expressed  in  the  formula: 

R  =  jK.  ~ 
a 

For  copper,  the  most  commonly  used  conductor,  the  value  of  K 
is  8.145  X  10~6  at  a  temperature  of  20°C.,  if  I  is  in  feet  and  a  in 
square  inches. 


GENERAL  PRINCIPLES  3 

However,  other  factors  than  those  mentioned  in  the  foregoing 
equation  also  affect  resistance.  The  most  important  of  these  is 
the  temperature.  In  the  case  of  the  common  metals,  the  resist- 
ance increases  with  the  temperature.  On  the  other  hand,  the 
resistance  of  electrolytes  decreases  as  the  temperature  rises,  and 
some  alloys  have  been  produced  whose  resistance  changes  but 
little  with  the  temperature.  Of  these  latter,  the  most  useful, 
perhaps,  is  manganin,  an  alloy  of  copper  and  manganese.  This 
metal  has  a  nearly  negligible  temperature  coefficient. 

Referring  again  to  the  metals  the  variation  with  tempera- 
ture may  be  expressed  approximately  by  the  formula: 

R  =  R0  (1  +  at) 

in  which  R  is  the  resistance  at  any  temperature,  R0  the  resistance 
at  0°C.,  and  t  is  the  temperature  in  degrees  C.  above  zero.  This 
formula  is  merely  approximate,  and  for  a  more  exact  expression 
it  would  be  necessary  to  employ  terms  of  the  second  and 
higher  degrees.  For  most  of  the  pure  metals,  including  copper, 
the  value  of  a  is  approximately  0.00427;  that  is,  the  resistance  of 
copper  increases  0.427  per  cent,  per  degree  rise  in  temperature, 
or  a  rise  of  2J^°  causes  an  increase  in  resistance  of  approximately 
1  per  cent. 

It  should  be  carefully  noted  that  the  resistance  does  not  change 
with  the  current,  as  is  frequently  the  case  with  similar  phe- 
nomena. Thus  the  magnetic  resistance  (called  reluctance)  of 
a  circuit  containing  iron  increases  with  the  magnetic  flux. 

4.  Resistors  in  Series  and  in  Parallel. — When  a  circuit 
contains  a  number  of  resistors  connected  in  series,  the  total 
resistance  of  the  circuit  is  the  sum  of  the  individual  resistances. 
Thus  if  Rij  R%,  Rs,  etc.,  are  the  different  resistances  and  if  R  is  the 
resistance  of  the  whole  circuit, 

R  =  Rl  +  £2  +  #3  + 

When  a  circuit  contains  a  number  of  resistors  in  parallel, 
the  total  current  flowing  in  the  circuit  will  be  the  sum  of  the 
currents  in  the  different  resistors.  Thus  in  Fig.  29,  the  current 
in  each  lamp  is  1  amp.  and  the  total  current  flowing  from  the 
generator  is  4  amp.  It  is  supposed  that  the  conductor  connecting 
the  different  resistors  has  itself  negligible  resistance.  If  this 
is  the  case,  it  is  evident  that  the  difference  of  potential  between 
the  ends  of  the  different  resistors  will  be  the  same.  Using  the 
same  nomenclature  as  before,  the  total  current  will  evidently  be 


4          PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

E  -7-  R,  where  R  is  the  resistance  of  the  whole  circuit,  and  the 
individual  currents  will  be  E  -f-  Ri,  E  -f-  R2,  etc.,  where  Ri 
R2,  etc.,  are  the  resistances  of  the  various  paths.  We  may  then 
write, 


And  dividing  by 


- 
xtl          zt 


or  in  words,  the  reciprocal  of  the  resistance  (the  conductance) 
of  a  number  of  resistors  in  parallel  is  equal  to  the  sum  of  the 
reciprocals  of  the  resistances  of  the  individual  resistors. 

Knowing  the  value  of  Ri,  R%,  etc.,  we  can  readily  compute  the 
value  of  R  from  the  above. 

5.  The  Wire  Table.  —  The  diameter  of  commercial  copper  wire 
is  measured  in  mils,  a  mil  being  0.001  in.  Thus  a  wire  0.1  in.  in 
diameter  would  have  a  diameter  of  100  mils.  The  cross  section 
of  wires  is  measured  in  circular  mils.  A  circular  mil  is  defined  as 
the  area  of  a  circle  0.001  in.  in  diameter.  So  if  a  wire  has  a 
diameter  of  100  mils,  its  area  is  10,000  circular  mils.  To  obtain 
the  cross  section  of  a  wire  in  circular  mils,  we  merely  square  its 
diameter  in  mils. 

The  sizes  of  the  different  wires  are  so  chosen  that  when  we 
pass  from  one  wire  to  the  one  having  the  next  smaller  number,  the 
cross  section  increases  approximately  26  per  cent.  *  If  we  pass  to 
a  wire  whose  number  is  three  less  the  cross  section  is  doubled. 
Thus  No.  7  wire  is  double  the  area  of  No.  10.  No.  4  wire  has 
four  times  the  cross  section  or  double  the  diameter  of  No.  10. 

It  is  a  simple  matter  to  reproduce  approximately  the  whole 
wire  table.  It  so  happens  that  the  resistance  of  a  copper  wire, 

1  mil  in  diameter,  and  1  ft.  long  is  10  ohms  at  a  temperature  of 
50°F.  (10°C.),     No.  10  wire  is  nearly  100  mils  in  diameter  (the 
exact  diameter  is  101.9  mils)  and  consequently  has  a  cross  section 
of  10,000  circular  mils.     Since  the  resistance  of  a  wire  varies 
directly  as  its  length  and  inversely  as  its  cross  section,  it  follows 
that  1000  ft.  of  No.  10  has  a  resistance  of  approximately  1  ohm. 
The  resistance  of  No.  11  is  26  per  cent,  greater,  or  1.26  ohms 
per   1000  ft.    That    of  No.    12   is    1.59   and   that   of   No.    13, 

2  ohms  per  1000  ft.     In  a  similar  way  we  could  readily  com- 
pute the  resistance  of  any  length  of  any  size  of  wire.     The 

*1.26  is  approximately  the  cube  root  of  2. 


GENERAL  PRINCIPLES  5 

foregoing  applies  only  to  the  Brown  &  Sharp  and  to  the  American 
wire  gages.  These  are  the  same  and  are  the  only  ones  used  to 
any  extent  in  this  country. 

6.  Magnetism. — Magnets  may  be  natural  or  artificial.  Thus 
there  is  a  magnetic  field  surrounding  the  earth,  the  lines  of 
magnetic  force  extending  from  the  region  surrounding  the  south 
pole  of  the  earth  to  the  region  surrounding  the  north  pole. 
Natural  magnets  or  loadstones,  consisting  of  an  oxide  of  iron, 
are  found  in  nature.  These  loadstones  are  comparatively  weak, 
so  for  commercial  purposes  use  is  made  of  pieces  of  hardened 
steel  which  have  been  made  magnetic  by  passing  current  through 
an  insulated  wire  wrapped  around  them.  If  the  magnet  must  be 
still  stronger,  soft  iron  is  substituted  for  the  steel.  The  iron 
magnet,  however,  loses  almost  all  of  its  magnetism  as  soon  as  the 
current  is  interrupted. 

A  magnet  exhibits  an  attraction  for  iron,  and  to  a  small  extent, 
for  allied  metals  like  nickel,  cobalt,  etc.  This  attractive  force  is 
somewhat  concentrated  in  two  or  more  regions  called  poles. 

If  the  action  of  two  magnets  on  one  another  be  tried,  we  find 
that  if  we  present  in  succession  each  pole  of  one  magnet  to  one 
pole  of  the  other,  there  is  a  strong  attraction  in  one  case  and  a 
repulsion  in  the  other  case.  By  using  a  third  magnet,  we  find 
that  two  poles,  both  of  which  are  attracted  by  one  pole  of  the 
third  magnet,  repel  one  another.  We  then  draw  the  conclusion 
that  like  poles  repel  one  another  and  unlike  poles  attract. 

To  define  strength  of  pole,  we  assume  that  we  can  have  one 
pole  of  a  magnet  so  far  removed  from  the  other  that  the  influence 
of  the  latter  is  negligible,  and  that  the  pole  is  concentrated  at  a 
point.  We  say  two  such  like  poles  have  unit  strength  if  they 
repel  one  another  with  a  force  of  1  dyne,  if  placed  1  cm.  apart 
in  air.  If  the  poles  had  been  unlike,  they  would  have  attracted 
one  another  with  a  force  of  1  dyne.  We  can  prove  by  experi- 
ment that  the 'force  exerted  is  proportional  to  the  strength  of 
each  pole  and  inversely  proportional  to  the  square  of  the  distance 
between  them.  We  then  have  the  fundamental  law  of  magnetic 
attraction  or  repulsion, 

_  ^1^2 
r* 

where  F  is  the  force  in  dynes,  r  the  distance  apart  of  the  poles 
in  centimeters,  and  mi  and  ra2  are  the  strengths  of  the  respective 
poles. 


6    .      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

7.  Strength  of  Field.  —  The  space  surrounding  a  magnet  is 
called  the  field  of  force.     We  define  the  strength  of  such  a  field 
at  a  given  point  by  saying  it  is  equal  to  the  force  exerted  by  it  on 
a  unit  pole  placed  at  the  point,  and  that  its  direction  is  that  in 
which  a  north  pole  is  urged.    The  strength  of  field  is  usually  desig- 
nated by  the  letter  5C. 

Flux  from  a  Unit  Pole.  —  Since  the  force  at  a  distance  of  1  cm. 
from  a  unit  pole  is  1  dyne,  there  must  be  a  strength  of  field  of 
1  line  per  square  centimeter  at  this  distance.  Since  the  area  of 
a  sphere  of  1  cm.  radius  is  4r,  it  follows  that  the  total  flux  of 
lines  of  force  from  a  unit  pole  is  47r. 

Lines  of  Force.  —  If  a  north  magnetic  pole  is  placed  in  the  field 
of  force  produced  by  another  magnet,  it  will  tend  to  move  in  a 
certain  direction.  This  direction  is  the  direction  of  the  field  of 
force  at  this  point.  To  a  certain  extent  the  field  of  force  can  be 
mapped  out  by  drawing  lines,  each  line  indicating  the  direction 
of  the  field,  or  the  direction  in  which  a  free  north  pole  would 
move  if  subject  to  the  influence  of  the  field  only. 

8.  Permeability.  —  If  in  place  of  air  we  substitute  a  magnetic 
substance  such  as  iron,  the  number  of  lines  of  flux  will  be  far 
greater  than  would  be  present  with  air.     The  ratio  of  the  number 
of  lines  present  with  the  iron,  to  the  number  present  with  air, 
is  called  the  permeability  of  the  iron.     If  we  designate  the  two 
quantities  respectively  by  (B  and  3C  we  have 

<B 


in  which  fj,  is  the  permeability. 

9.  Generation  of  Electromotive  Force.  —  It  was  discovered 
early  in  the  history  of  electricity  that  an  e.m.f.  and  consequently 
a  current  can  be  generated  by  the  relative  motion  of  a  magnet 
and  an  electric  circuit.  Thus  in  Fig.  1,  let  the  conductor  AB  be 
capable  of  sliding  upon  the  circuit,  CDE,  and  let  there  be  a 
magnetic  flux  of  strength  (B  perpendicular  to  the  paper.  If  the 
wire  AB  be  moved  either  to  the  right  or  to  the  left,  there  will  be 
generated  in  it  an  e.m.f.  Experiment  shows  that  the  value  of 
this  e.m.f.  is  given  by  the  very  simple  rule  that  it  is  equal  in 
absolute  units,  to  the  number  of  lines  cut  per  second.  In  volts 
it  is  this  value  divided  by  100,000,000  or  108.  If  several  con- 
ductors are  connected  in  series,  the  e.m.f.  generated  will  be  pro- 
portionally increased.  If  I  is  the  length  of  the  conductor  in 


GENERAL  PRINCIPLES 


centimeters,  and  the  average  value  of  the  flux  per  square  centi- 
meter is  (B,  then  N  conductors  moving  with  a  velocity  of  v  centi- 
meters per  second  will  generate  an  e.m.f.  in  volts  equal  to 


E  =  Nl&v  +  108  =  N3>8  -r-  108  = 

in  which  3>s  is  the  flux  cut  in  1  sec.  and  $  is  the  total  flux 
cut  in  time  t.  In  the  foregoing  equation  we  assume  that  the 
motion  is  uniform.  If  the  motion  of  the  conductors  is  variable, 
or  if  the  flux  varies  from  point  to  point,  we  must  find  the  instan- 
taneous rate  of  cutting.  We  must  then  consider  the  very  small 
flux  cut  dp  during  the  very  short  interval 
of  time  dt  and  we  obtain  the  expression 


B 


This  holds  true  no  matter  how  the  flux 
or  the  motion  varies.     It  is  then  the  uni- 
versal   equation    of    the    generation    of 
e.m.f.  by  the  cutting  of  lines  of  induc- 
tion by  conductors,  or  of  conductors  by  FIG.  1. 
lines  of  induction.     It  is  entirely  inde- 
pendent of  the  current  flowing,  and  in  fact  it  is  not  even  nec- 
essary that  the  circuit  be  closed. 

The  direction  of  the  induced  e.m.f.  is  readily  found  by  placing 
the  thumb,  index-finger  and  middle  finger  of  the  right  hand,  ap- 
proximately at  right  angles  to  one  another.  If  we  point  the  in- 
dex-finger in  the  direction  of  the  flux,  and  the  thumb  in  the  direc- 
tion of  the  motion,  the  middle  finger  will  indicate  the  direction 
of  the  induced  e.m.f. 

10.  Force  on  a  Conductor  in  a  Magnetic  Field. — It  was  also 
noticed  early  that  a  conductor  like  that  of  Fig.  1  lying  in  a 
magnetic  field  and  carrying  current  was  subject  to  a  force  tend- 
ing to  move  it  across  the  lines  of  induction.  In  the  figure  as 
shown,  this  would  be  to  the  right  or  left.  This  force  is  propor- 
tional to  the  current  flowing,  to  the  number  of  conductors  in- 
volved, to  the  strength  of  the  field  and  to  the  length  of  the  wire. 
We  may  then  write, 

F  =  NK&I 

In  which  I  is  in  centimeters,  /  is  in  absolute  units  of  current,  and 
F  is  in  dynes.     N  is  the  number  of  conductors.     If  /  be  expressed 


8          PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

in  amperes,  the  force  will  be  one-tenth  as  great.     This  force  is 
not  influenced  by  the  material  of  the  wire,  the  velocity  at  which 
it  moves,  etc.     Indirectly,  it  may  be  influenced  by  these  factors, 
since  they  may  act  to  change  the  current  or  the  magnetic  field. 
The  above  expression  may  be  readily  reduced  to 


in  which  F  is  in  pounds,  I  is  in  inches,  /  is  in  amperes  and  (B  is 
in  lines  per  square  inch. 

The  direction  in  which  the  force  is  exerted  may  be  determined 
by  placing  the  thumb,  index-finger  and  middle  finger  of  the  left 
hand,  approximately  at  right  angles  to  one  another.  If  we  point 
the  index-finger  in  the  direction  of  the  flux,  and  the  middle 
finger  in  the  direction  of  the  current,  the  thumb  will  indicate  the, 
direction  of  the  motion. 

11.  Work.  —  The  work  done  is  the  product  of  the  force  and  the 
distance  the  conductor  moves.  Thus,  if  the  conductor  in  the 
foregoing  case  is  moved  a  distance,  d,  the  work  done  expressed 
in  c.g.s.  units  (ergs)  will  be  (considering  only  one  conductor) 

W=Fd  =  Il($>d  =  I$  or  expressing  I  in  amperes  and  W  in  joules 

W  =  /<£  -T-  108 

or  the  work  done  is  the  product  of  the  current  and  the  flux  cut. 

Power.  —  The  power  is  the  rate  of  doing  work,  or  it  is  the  work 
divided  by  the  time,  and  is  expressed  in  watts.  Thus 

W 
P       T    = 


or  the  power  in  an  electric  circuit  is  the  product  of  the  current 
and  the  e.m.f. 

12.  Solenoids.  —  The  word  solenoid  is  derived  from  a  Greek 
word  signifying  a  pipe.  A  solenoid  is  shown  in  Fig.  2.  If  a 
current  be  passed  through  the  turns,  a  magnetic  flux  will  be  set 
up  with  approximately  the  distribution  shown.  This  solenoid 
will  act  much  like  a  bar  magnet.  One  end  will  attract  the  north 
pole  of  a  permanent  magnet  and  repel  the  south  pole.  If  mounted 
in  such  a  manner  that  it  is  free  to  move  about  a  vertical  axis,  it 
will  tend  to  set  itself  in  a  north  and  south  direction  in  the  same 
manner  as  a  compass  needle  does.  If  a  core  of  iron  be  substi- 
tuted for  the  air,  the  magnetic  effects  will  be  greatly  intensified, 


GENERAL  PRINCIPLES 


9 


and  if  the  core  be  made  continuous  so  as  to  surround  the  coils, 
the  flux  will  have  a  continuous  iron  path,  and  it  will  become  still 
greater. 

The  direction  of  the  magnetic  force  may  be  determined  by 
grasping  the  solenoid  with  the  right  hand,  the  fingers  pointing 
in  the  direction  of  the  current.  The  thumb  will  then  indicate 


FIG.  2. 

the  direction  of  the  magnetic  force  and  will  point  toward  the 
north  pole. 

13.  Force  in  a  Solenoid. — To  determine  the  magnetic  force  at 
any  point  in  a  solenoid,  let  us  suppose  that  the  solenoid  is  of 
infinite  length.  In  Fig.  3  let  a  unit  magnetic  pole  be  located 
inside  the  solenoid  at  the  end  of  the  dotted  line  A.  As  we  have 
previously  shown,  4?r  lines  will  emanate  from  the  unit  mag- 


o    o    o    o 


A 
I 

O    |O 

I 
I 


OOiOOOOOO 


oooooooooooooo 
FIG.  3. 

netic  pole.  If  we  have  a  current,  /,  in  the  wires  of  the  solenoid, 
and  move  the  pole  1  cm.  along  the  axis  of  the  solenoid,  the  work 
done  will  be  the  product  of  the  lines  cut,  times  the  current,  times 
the  number  of  wires  carrying  the  current  or 

W    =    47Ttt/ 

in  which  n  is  the  number  of  conductors  per  centimeter  length  of 
the  solenoid.  Since  work  is  the  product  of  force  and  distance, 


10        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

and  since  the  distance  was  assumed  to  be  1  cm.,  the  force  and 
the  work  will  be  the  same,  or  F  =  47rnl  or  if  /  is  in  amperes, 
F  =  47m/  -T-  10. 

14.  Magnetomotive  Force. — The  magnetomotive  force  (in  a 
magnetic  circuit),  is  the  line  integral  of  the  force  taken  around 
the  circuit,  or  it  is  the  work  done  in  moving  a  unit  magnetic  pole 
around  the  circuit.  The  simplest  way  of  deriving  an  expression 
for  this  is  to  imagine  the  solenoid  bent  around  into  the  form  of  a 
ring  as  shown  in  Fig.  4.  The  mean  magnetic  path  around  the 
ring  is  I  cm.  The  force  at  any  point  will  be  given  by  the  same 
expression  as  before.  The  work  done  will  be  equal  to  the 

force  times  the  length  of  the  ring. 
The  turns  per  centimeter  times  the 
length  of  the  ring  is,  however,  the 
total  number  of  turns  in  the  solenoid. 
Calling  this  value  N  we  have 


m.m.f.  =  4irnll  •*•  10  =  kirNI  -f-  10 
=  1.257A7 

The  quantity  NI  is  called  the  am- 
pere    turns.      The    magneto-motive 
FIG.  4.  force  is  the  same  for  a  large  current 

and  a  small  number  of  turns  or  for 

a  small   current   and   a  large   number   of  turns,  provided  the 
product  is  the  same. 

15.  Magnetic  Circuit.  —  A  magnetic  circuit,  like  an  electric 
circuit,  is  always  closed,  that  is,  each  line  of  magnetic  flux  must 
return  to  its  starting  point.  Thus,  the  total  flux  of  induction 
across  any  section  of  the  circuit  must  be  the  same,  although  the 
flux  density  in  the  different  parts  may  vary  widely.  By  the 
flux  density  we  mean  the  number  of  lines  of  flux  crossing  a 
square  centimeter,  the  section  being  taken  perpendicular  to  the 
flux.  We  usually  designate  the  flux  density  by  the  letter  (B, 
and  have  the  relation 


The  general  law  of  the  magnetic  circuit  is  like  that  of  the 
electric  circuit  and  is  expressed  by  the  relation 

,       _  Magnetomotive  force 
Reluctance 


GENERAL  PRINCIPLES  11 

The  method  of  determining  the  magnetotomotive  force  has 
already  been  explained.  The  reluctance  is  similar  to  the  electric 
resistance  of  a  circuit,  and  is  determined  by  a  formula  of  the 
same  nature.  If  several  different  materials  in  series  compose 
the  magnetic  circuit,  we  have 

Reluctance  =  -  -  +  — --  +    .    .    .    . 


where  Zi,  Z2,  etc.,  are  the  lengths  in  centimeters  of  the  various 
parts  of  the  circuit;  01,  a2,  etc.,  are  the  areas  in  square  centi- 
meters; and  MI,  fjL2,  are  the  permeabilities  of  the  various  materials. 
If  one  of  these  is  air;  M  becomes  unity.  We  may  then  write 
the  equation  for  the  total  flux  in  a  circuit  as  follows: 

1.257NI 


It  will  be  noted  that  this  is  essentially  the  same  equation 
used  in  determining  the  total  current  in  an  electric  circuit. 
The  more  complicated  form  in  which  it  is  written  is  due  to  the 
fact  that  we  have  no  convenient  means  of  measuring  directly  the 
m.m.f.  or  the  reluctance  of  a  circuit,  whereas  we  can  readily 
measure  the  e.m.f.  or  the  resistance  of  an  electric  circuit.  In 
the  magnetic  circuit  it  is,  therefore,  usually  necessary  to  compute 
the  values  of  the  m.m.f.  and  the  reluctance. 

It  should  also  be  noted  that  while  in  the  electric  circuit  we  have 
a  great  range  of  specific  resistance,  varying  from  that  of  almost 
perfect  insulators  to  the  low  specific  resistance  of  copper  and 
silver,  there  is  no  such  range  in  the  magnetic  reluctance  of  various 
materials.  The  great  mass  of  matter  falls  in  the  one  class  and 
has  a  permeability  the  same  as  air,  namely,  unity.  We  have  a 
small  class  of  materials  of  which  the  permeability  is  slightly  less 
than  unity,  and  another  small  group  with  a  permeability  of  more 
than  unity.  Of  these,  the  only  ones  of  commercial  importance 
are  iron  and  its  alloys.  These  may  have  a  permeability  as  high 
as  3000  or  more,  or  at  excessive  densities  nearly  as  low  as  unity. 

16.  Variation  of  Permeability. — The  last  sentence  will  serve 
to  indicate  another  striking  difference  between  magnetic  reluc- 
tance and  electric  resistance.  The  latter  is  not  at  all  affected 
by  the  value  of  the  current  strength.  The  former  is  decidedly 
so  affected.  In  general,  the  permeability  increases  somewhat  as 


12        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

the  flux  density  is  gradually  increased  from  zero  to  a  small 
value.  A  further  increase  in  the  flux  density  results  in  a  de- 
crease in  the  permeability.  This  is  well  shown  for  several 
materials  in  the  curves  of  Fig.  5.  These  also  serve  to  indicate 
roughly  the  usual  limits  of  the  flux  density  per  square  inch. 
The  term  kilomaxwell  means  1000  lines  of  induction. 


2400 
2200 
2000 
1800 


1600 


^1400 
1 1200 


800 


400 


200 


tlron 


\ 


\ 


5      6       7      8       9     10     11     12     13     14     15     18     17     18     19    20(55 
Kilomaxwells  per  Square  Centimeter 

FIG.  5. 


17.  Magnetization  Curves. — If  we  consider  a  magnetic  circuit 
of  uniform  cross  section  and  composed  of  the  same  material  through- 
out, we  may  write  the  equation  for  the  total  flux  in  the  form 


I 

If  we  divide  both  sides  of  this  equation  by  the  area  a  and  con- 
sider a  length  of  only  one  centimeter  of  the  circuit,  we  have 

®  =  —  =  1.257AT/M 

in  which  (B  is  the  flux  density  and  NI  is  the  ampere  turns  required 
to  produce  a  flux  density  of  (B  in  1  cm.  of  the  material. 

The  most  convenient  way  of  expressing  the  magnetic  proper- 
ties of  a  given  material  is  to  give  the  ampere  turns  required  per 
centimeter  (or  per  inch)  for  a  given  number  of  lines  per  square 
centimeter  (or  per  square  inch). 


GENERAL  PRINCIPLES 


13 


The  curves  of  Fig.  6  show  the  magnetic  properties  of  sheet 
steel,  cast  steel,  and  cast  iron,  the  materials  most  used  in  the 
construction  of  magnetic  circuits.  The  flux  is  shown  in  lines 
per  square  inch  and  the  magnetizing  force  in  ampere  turns  per 
inch  length. 

The  usual  flux  densities  employed  are  about  85,000  lines  per 
square  inch  in  cast  steel,  from  90,000  to  as  high  as  120,000  in  sheet 
steel,  and  about  40,000  in  cast  iron.  Usually  it  does  not  pay  to  go 
higher  on  account  of  the  great  number  of  ampere  turns  required. 


140 


120 


100 


js  iw 7^ 

i    \L 

w    80  k-// 


Cast  St 


60 


Cast  Iron 


4Q| 


20 


ICO  200  300  400  500 

Ampere  Turns  per  Inch  Length 

FIG.  6. 


700 


Residual  Magnetism. — In  Fig.  6,  with  zero  ampere  turns  the 
flux  is  also  zero.  If,  however,  a  piece  of  iron  be  magnetized  and 
the  exciting  current  then  interrupted  it  will  be  found  that  a 
certain  portion  of  the  magnetism  remains.  In  general,  the 
amount  will  be  greater  the  harder  the  iron.  With  magnet  steel, 
prepared  for  this  purpose,  a  large  amount  remains,  so  that  we 
have  a  permanent  magnet.  All  steel  and  iron  retain  some 
magnetism.  The  flux  which  remains  in  the  iron  is  called  the 
residual  magnetism. 

PROBLEMS 

1.  What  current  will  an  e.m.f.  of  110  volts  force  through  a  resistance  of 
125  ohms? 


14:        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

2.  A  certain  incandescent  lamp  connected  to  a  220-volt  circuit  takes  a 
current  of  0.333  amp.     What  is  the  resistance  of  the  lamp? 

3.  Three  resistors  of  10,  30  and  57  ohms  are  connected  in  series.     With 
a  current  of  2  amp.  passing,  what  is  the  e.m.f.  applied  to  the  circuit?     What 
is  the  drop  over  each  of  the  resistances? 

4.  The  armature  of  a  certain  dynamo  has  a  resistance  of  0.04  ohm  at 
0°C.     What  is  its  resistance  at  75°C.?     With  a  current  of  50  amp.  flowing, 
what  is  the  power  loss  at  0°?     At  75°? 

6.  In  the  above,  what  e.m.f.  is  required  to  force  the  current  through  the 
armature  at  0°?     At  75°? 

6.  A  certain  shunt-field  winding  has  a  resistance  of  100  ohms  at  a  room 
temperature  of  30°C.     With  the  machine  hot  the  resistance  of  the  field  is 
110  ohms.     What  is  the  temperature  of  the  machine?     With  an  applied 
e.m.f.  of  220  volts,  what  is  the  power  loss  at  30°C.  and   at  the  operating 
temperature  just  found? 

7.  Two  poles  of  strengths  10  and  15  are  at  a  distance  of  20  cm.  in  air. 
What  is  the  attraction  or  repulsion  between  them  in  dynes? 

8.  A  certain  solenoid  is  100  cm.  long  and  is  uniformly  wound  with  1000 
turns  of  wire  carrying  5  amp.     What  is  the  magnetic  force  in  the  solenoid? 
What  is  the  m.m.f.? 

9.  A  ring  of  iron  of  a  cross  section  of  2  sq.  in.  has  a  mean  length  of  25  in. 
It  is  uniformly  wound  with  2000  turns  of  wire  carrying  a  current  of  0.85 
amp.     What  is  the  magnetic  flux  in  the  iron  if  its  permeability  is  400? 
What  is  the  flux  density? 

10.  What  will  be  the  flux  in  the  above  ring  if  the  iron  is  replaced  by  air? 
By  brass?     By  wood? 

11.  The  foregoing  ring  is  cut  across  at  right  angles  to  its  axis  and  the 
ends  spread  so  that  an  air  gap  of  0.1  in.  is  interposed,  the  length  of  iron  re- 
maining the  same.     What  will  be  the  flux,  the  permeability  being  1000  and 
all  other  conditions  remaining  the  same?     What  current  will  be  required  in 
order  that  the  flux  may  be  the  same  as  in  Example  9,  the  permeability 
being  400? 


CHAPTER  II 
ELECTRIC  MOTORS 

18.  Elementary  Form  of  Electric  Motor. — One  of  the  simplest 
possible  forms  of  the  electric  motor  is  illustrated  in  Fig.  7. 
It  is  hardly  suitable  for  commercial  use,  but  serves  well  to  illus- 
trate some  of  the  principles  already  studied.  Motors  of  this 
type  are  frequently  sold  as  toys.  The  rotating  part  consists  of 
a  cross-shaped  piece  of  soft  iron  or  steel.  While  the  one  shown 
in  the  illustration  has  four  arms,  either  a  greater  or  a  lesser 
number  may  be  used.  The  rotating  part  is  carried  on  a  shaft 
supported  in  suitable  bearings,  and  rotates  between  the  poles  of 


FIG.  7. 

an  electromagnet  N  —  S.  The  magnet  is  wound  with  wire  as 
shown.  The  current  may  be  supplied  from  a  battery  or  other 
suitable  source.  The  path  of  the  current  is  from  the  battery 
to  a  spring  or  brush  B,  through  the  cam  C  to  the  shaft,  and  by 
means  of  a  sliding  contact  to  the  winding  of  the  magnet  through 
the  switch  £',  and  so  back  to  the  battery. 

In  the  position  shown  the  brush  is  just  about  to  make  contact 
with  the  cam,  thus  closing  the  circuit.  As  soon  as  this  occurs  the 
projection  1  will  be  attracted  to  the  pole  S  and  the  projection  3 
to  the  pole  N.  This  will  continue  until  1  and  3  are  directly  in 

15 


16        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


line  with  N  and  S.  At  this  instant  the  cam  should  have  rotated 
just  far  enough  so  that  the  contact  between  itself  and  the  brush 
is  broken.  The  rotating  part  will  then  be  carried  on  by  its 
momentum  until  pole  4  is  in  about  the  same  position  as  that 
occupied  by  pole  1  in  the  figure.  At  this  instant  the  contact 
will  again  be  made  by  the  cam  and  the  process  will  be  repeated. 
It  will  be  noted  that  the  torque  or  turning  effort  on  the  shaft 
of  this  motor  is  not  constant  but  is,  in  fact,  zero  during  a  part  of 
the  revolution.  This  in  itself  would  not  be  a  serious  matter,  at 
least  at  reasonably  high  speeds,  because  the  momentum  of  the 
rotating  part  would  be  sufficient  to  keep  the  motion  practically 
uniform.  The  fact,  however,  that  the  torque  is  not  constant 

means  that  the  motor  will  not  al- 
ways be  self-starting.  If  it  stopped 
in  such  a  position  that  the  brush 
was  'in  contact  with  the  spring  it 
would  start  itself  when  the  switch  was 
closed,  but  if  the  brush  was  not  in 
contact  no  current  would  pass  and 
there  would  be  no  tendency  to  turn. 
Perhaps  an  even  greater  defect  of  this 
motor  from  the  practical  standpoint 
is  the  fact  that  it  sparks  badly  at  the 
contact  between  the  brush  and  the 
cam.  A  current  flowing  in  a  wire 
FIG.  8.  possesses  a  property  very  similar  to 

a  mass  of  matter  in  motion,  namely, 

it  resists  very  strongly  any  tendency  to  force  it  to  stop  sud- 
denly. Matter  manifests  this  property  by  the  development  of 
great  force  and  heat;  the  electric  current  by  the  development  of 
an  electric  arc  and,  of  course,  also  by  the  production  of  heat. 
This  phenomenon  will  be  more  fully  treated  later. 

19.  The  Armature. — The  ordinary  electric  motor  is  a  more 
advanced  type  than  the  one  just  considered.  While  the  machine 
will  be  described  as  a  motor,  the  same  machine  without  any 
change  whatever  will  also  operate  as  an  electric  generator.  The 
reason  for  this  will  appear  presently.  In  fact,  this  is  a  general 
rule.  It  will  be  found  that  any  motor,  whether  for  alternating 
current  or  for  direct  current,  will  also  operate  as  a  generator. 

In  Fig.  8  is  shown  a  split  ring  wound  with  insulated  wire. 
It  will  be  seen  that  the  wire  is  wound  continuously  around  the 


ELECTRIC  MOTORS 


17 


ring  in  the  same  direction.  At  two  opposite  points  connections 
are  made  to  the  wires  from  a  battery  or  other  source  of  continu- 
ous current.  As  shown,  the  positive  pole  of  the  battery  is 
connected  to  the  lower  lead.  Here  the  current  divides  into  two 
equal  parts,  half  flowing  through  the  left  half  of  the  ring  and  half 
through  the  right  half.  If  we  consider  for  the  moment  only  one- 
half  of  the  ring,  say  the  left  half,  it  is  apparent  that  it  will  become 


FIG.  9. 

a  magnet  as  soon  as  the  current  passes  through  the  winding, 
and  by  making  use  of  the  rule  that  if  we  grasp  the  ring  with  the 
right  hand,  the  fingers  pointing  in  the  direction  of  the  current 
flow,  the  thumb  will  indicate  the  north  pole,  it  will  be  seen  that 
the  upper  end  of  the  ring  will  be  a  north  pole  and  the  lower  end 
a  south  pole. 

If  we  consider  the  right  half  of  the  ring  and  apply  the  same  rule 
to  it,  it  will  be  apparent  that  the  upper  pole  is  likewise  north  and 


18       PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

the  lower  pole  south.  If  now  the  ring  should  be  joined  at  the 
split  part  so  as  to  form  a  complete  ring,  we  should  have  a  north 
pole  at  the  top  and  a  south  pole  at  the  bottom,  each  of  these 
being  due  to  the  combined  action  of  the  two  poles  present  in 
the  split  ring. 

In  Fig.  9  is  shown  a  ring  of  this  character.  The  ring  is  so 
mounted  on  a  shaft  that  it  is  free  to  rotate.  Brushes  marked  + 
and  —  are  arranged  to  make  contact  with  the  winding  even 
though  the  ring  is  rotating.  It  is  supposed  that  the  wire  is  so 
arranged  that  the  surface  is  smooth,  so  that  the  brush  may  make 
good  contact  at  all  times.  If  current  is  passed  through  the 
winding  of  the  ring  by  means  of  the  brushes,  it  will  be  seen  that 
we  shall  have  a  N  pole  at  the  top  of  the  ring  and  a  S  pole  at  the 
bottom.  This  will  be  true  even  though  the  ring  is  in  motion. 
The  poles  will  therefore  stand  still  while  the  ring  rotates.  A  ring 
arranged  in  this  manner  is  called  an  armature. 

20.  The  Field  Magnet. — Surrounding  the  armature  are  shown 
the  poles  of  a  horseshoe  magnet.     This  is  commonly  called  the 
field  magnet   or   simply   the  field.     The   current    is    carried    a 
number  of  times  around  the  field  as  shown,  thus  strongly  mag- 
netizing it.     This  is  called  a  series  connection  and  the  motor  is 
known  as  a  series  motor. 

21.  Operation  as  a  Motor. — The  action  of  the  machine  as  a 
motor  will  now  be  readily  understood.     When  current  is  passed 
through  it,  the  upper  part  of  the  armature  will  become  a  N  pole 
and  the  lower  part  a  S  pole.     At  the  same  time  we  have  a  N 
and  a  S  pole  in  the  field.     It  will  be  evident  that  the  S  pole  of  the 
armature  will  be  attracted  toward  the  N  pole  of  the  field,  and  the 
N  pole  of  the  armature  toward  the  S  pole  of  the  field.     At  the 
same  time  the  N  pole  of  the  field  will  repel  the  N  pole  of  the 
armature  and  the  S  pole  of  the  field  will  repel  the  S  pole  of  the 
armature.     All  these  four  actions  tend  to  turn  the  armature  in 
the  same  direction.     The  top  of  the  armature  will  move  to  the 
left  as  shown,  or  the  armature  will  turn  in  a  counter-clockwise 
direction. 

When  the  armature  first  starts  to  turn,  its  poles  will  move  a 
short  distance  with  it.  However,  before  the  armature  has 
turned  through  any  great  angle,  the  brush  will  cease  to  make 
contact  with  the  wire  it  touched  at  first  and  the  next  turn  will 
slide  under  the  brush.  As  soon  as  this  takes  place  the  pole  will 
move  backward  to  the  position  it  occupied  originally.  Thus 


ELECTRIC  MOTORS 


19 


no  matter  how  rapidly  the  armature  may  rotate  the  pole  will 
stand  nearly  still,  having  merely  a  slight  backward  and  forward 
motion.  The  machine  will  therefore  continue  to  operate  as  a 
motor  as  long  as  current  is  supplied  to  it. 

It  will  also  be  seen  that  this  motor  will  have  no  dead  points, 
that  is  to  say,  it  will  start  from  rest  no  matter  what  the  position 
of  the  armature.  Therefore  it  is  greatly  superior  in  this  respect 
to  the  motor  illustrated  in  Fig.  6.  Moreover,  the  turning  effort 
(which  we  call  torque)  will  be  constant  during  the  entire  rota- 
tion. This,  although  a  minor 
point,  is  of  importance  in  some 
applications. 

22.  The  Commutator.— A  few 
years  ago  many  machines  were 
constructed  with  the  brushes  trail- 
ing upon  the  winding  exactly  as 


FIG.  10. 


FIG.  11. 


shown.  Others  were  constructed  with  the  brushes  bearing  upon 
the  side  of  the  winding.  At  the  present  time,  this  construction 
is  rarely  if  ever  used.  It  has  been  found  cheaper  and  equally 
as  efficient  to  provide  a  separate  structure  to  make  contact  with 
the  brushes.  This  structure  is  known  as  the  commutator. 
Figure  10  shows  an  armature  with  a  commutator.  The  latter 
consists  of  a  number  of  bars  of  copper  mounted  upon  a  sleeve. 
All  the  bars  are  insulated  from  one  another  and  from  the  sleeve. 
Each  bar  is  connected  to  a  turn  of  the  winding.  There  may  be  as 
many  bars  as  there  are  turns  in  the  windings,  at  least  in  the  case 
of  large  machines.  In  small  machines  there  are  frequently  a 
great  many  turns  for  each  commutator  bar.  The  action  of  the 
machine  is  exactly  the  same  as  before. 


20        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


23.  Action  of  the  Forces  on  the  Conductors  of  a  Motor. — The 

foregoing  way  of  looking  at  the  action  of  a  direct-current  motor, 
while  simple,  is  open  to  some  objection.  For  example,  it  is  en- 
tirely possible  to  neutralize  the  "  poles  "  of  the  armature  by  means 
of  a  compensating  winding  (see  Art.  294),  and  the  motor  will 
still  operate.  Figure  11  will  serve  to  give  a  more  accurate  idea 
of  the  actions  which  actually  take  place. 

The  currents  in  the  armature  are  represented  by  small  crosses 
and  by  small  circles.  The  cross  indicates  a  current  from  the 
observer;  the  circle  a  current  toward  him.  The  reader  may 
readily  remember  this  by  considering  the  cross  as  the  feathers  on 
the  end  of  an  arrow.  It  will  be  seen  that  the  currents  flow  in 
the  same  direction  as  in  Fig.  9. 

24.  Force  Acting  upon  a  Current  in  a  Magnetic  Field. — To 
understand  the  action  of  these  currents  upon  the  magnetism, 


N 


FIG.  12. 


FIG.  13. 


let  us  consider  Figs.  12,  13  and  14.  In  Fig.  12  is  shown  the 
magnetic  field  between  two  opposite  poles,  the  direction  of  the 
flux  being  from  north  to  south  as  shown.  Figure  13  shows  the 
magnetic  field  which  surrounds  a  conductor  carrying  a  current  of 
electricity.  The  lines  of  flux  are  circles  having  the  direction 
shown  and  placed  closer  together  near  the  wire.  Figure  14 
shows  the  field  produced  by  the  combination  of  these  two  ele- 
ments. The  lines  of  magnetism  are  close  together  just  above 
the  wire  since  the  magnetic  effect  of  the  current  in  the  wire 
and  the  magnetic  field  are  both  in  the  same  direction.  Just 
below  the  wire  there  is  little  or  no  magnetism  since  the  effects 
are  in  opposite  directions.  Since  the  lines  of  magnetism  act 
like  stretched  elastic  bands,  there  will  be  a  force  acting  on  the 
wire  and  tending  to  force  it  downward  out  of  the  field.  There 
will  be  an  equal  and  opposite  force  tending  to  force  the  magnet 


ELECTRIC  MOTORS  21 

upward.     Either  the  wire  or   magnet  or   both  may  move,  de- 
pending upon  which  one  is  free. 

The  force  which  acts  upon  the  wire  and  the  magnet  will  be 
proportional  to  the  strength  of  the  magnetic  field,  to  the  current 
in  the  wire  and  to  the  length  of  the  wire  that  is  exposed  to  the 
magnetic  field.  Obviously,  where  a  number  of  wires  are  acting, 
the  total  force  will  also  be  proportional  to  the  number  of  wires. 

Returning  now  to  Fig.  11  we  can  readily  see  why  the  arma- 
ture should  rotate.     All  the  wires  in  the  gap  on  the  left  are  carry- 
ing current  toward  the  observer,  and  all  will  be  pushed  downward 
by    the    magnetic    field.     All    of 
those    on    the    right   are   carrying 
current  from  the  observer,  and  all 
will  be  pushed  upward.     Both  of 
these  actions  tend  to  turn  the  ar- 
mature in  a  counter-clockwise  di- 
rection as  shown      Since  the  posi-  FlG 
tion  of  the  currents  is  not  changed 
as  the  armature  rotates,  the  action  will  be  continuous. 

It  will  be  seen  that  the  conductors  on  the  inside  of  the  armature 
are  not  in  the  magnetic  field.  It  is  true  that  a  few  lines  of  mag- 
netism may  leak  across  this  space,  but  the  field  will  be  very  weak 
and  practically  negligible.  Since  these  conductors  are  not  in 
the  field  the  force  upon  them  will  be  zero.  Therefore  they  have 
no  part  in  the  action  except  that  they  carry  the  current  from  one 
active  conductor  to  the  next. 

25.  Multipolar  Machines. — All  the  machines  we  have  con- 
sidered have  had  two  poles.  Commercial  machines,  except  in 
the  smallest  sizes,  have  in  general  four  or  more  poles.  This 
leads  to  a  more  symmetrical  structure  and  is  stronger  and  better 
mechanically.  It  can  also  be  shown  that  the  weight  of  iron  or 
steel  in  the  field  is  greatly  reduced,  thus  leading  to  a  cheaper 
and  lighter  machine.  A  multipolar  machine  is  illustrated  in 
Fig.  18. 

28.  Construction  of  the  Drum-wound  Armature. — The  ring 
winding  just  described  has  one  fatal  defect  which  has  caused  it 
to  become  practically  obsolete.  In  winding,  it  is  necessary  to 
carry  each  of  the  wires  through  the  armature,  one  at  a  time,  by 
hand.  This  is  a  slow  and  laborious  process  not  adapted  to 
modern  methods  of  manufacture.  The  winding  that  is  in  almost 
universal  use  is  called  the  drum  winding.  All  the  coils  are 


22        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

wound,  and  in  most  cases  fully  insulated,  before  being  placed  on 
the  outside  of  the  armature  core.     The  appearance  of  typical 
coils  may  be  seen  from  Fig.  15.     There  may  be  only  one  turn  of 
wire  in  a  coil  although  several  are  usual. 
The  surface  of  the  armature  is  practically  always  slotted  and 


FIG.  15. 


the  coils  are  placed  in  the  slots.  There  are  a  number  of  reasons 
for  doing  this.  Winding  is  somewhat  easier  since  the  coils  are 
held  firmly  in  place  while  the  connections  are  being  made.  The 
completed  armature  is  far  less  likely  to  be  injured  by  being  placed 
on  the  floor  or  by  being  struck  accidentally.  Perhaps  the  most 


ELECTRIC  MOTORS  23 

obvious  advantage  of  the  slotted  construction  is  the  fact  that 
the  air  gap  may  be  made  far  shorter  than  would  be  possible  if 
the  coils  were  placed  on  the  outside.  It  will  be  remembered  that 
the  permeability  of  air  is  unity,  while  that  of  iron  at  ordinary 
flux  densities  is  about  1000.  Therefore  a  far  greater  number  of 
ampere  turns  is  required  to  force  flux  at  a  given  flux  density 
across  an  air  gap  than  is  required  for  the  same  flux  density 
through  the  same  length  of  iron.  Hence  it  is  desirable  that  the 
gap  be  kept  short  so  that  the  number  of  turns  required  upon  the 
field  may  be  small.  However,  one  should  not  infer  from  the 
foregoing  that  it  is  desirable  to  make  the  gap  as  short  as  it  can 
possibly  be  made  and  still  give  the  necessary  clearance.  If  this 
were  done  the  number  of  turns  required  upon  the  field  to  force 
the  flux  across  the  gap  would  be  small  compared  with  the  number 
of  turns  upon  the  armature,  and  in  consequence  the  distortion 
of  the  flux  would  be  too  great.  Consequently,  the  gap  is  made 
comparatively  great,  but  by  no  means  so  long  as  would  be  neces- 
sary if  the  winding  were  placed  upon  the  outside  of  the  armature. 

27.  Connections  of  a  Lap-wound  or  Parallel-wound  Arma- 
ture.— The  number  of  turns  in  a  coil  is  usually  such  that  a  coil 
fills  only  half  the  available  space  in  a  slot.  Each  slot,  therefore, 
contains  one  side  of  each  of  two  coils.  •  The  coils  are  arranged  in 
a  perfectly  symmetrical  manner  so  that  one  side  of  each  coil 
occupies  the  upper  half  of  a  slot  while  the  other  side  is  in  the 
lower  half  of  another  slot,  distant  approximately  one  pole  pitch. 
The  coils  are  so  connected  to  the  commutator  that  if  the  begin- 
ning of  a  coil  is  connected  to  bar  No.  1,  the  end  is  connected  to 
bar  No.  2.  The  beginning  of  the  next  coil  is  then  also  connected 
to  bar  No.  2  and  the  other  end  of  this  second  coil  to  bar  No.  3. 
This  constitutes  a  lap  winding. 

These  connections  are  clearly  shown  in  Fig.  16.  This  is  sup- 
posed to  represent  a  four-pole  armature  flattened  out,  or  we  may 
think  of  it  as  being  a  portion  of  a  very  large  armature  having  a 
great  number  of  poles,  so  great  in  fact  that  a  small  section  of  the 
armature  is  practically  straight.  Starting  from  one  of  the 
brushes,  say  A,  the  current  divides  into  two  parts,  half  going  to 
the  left  and  half  to  the  right.  If  we  trace  the  path  of  the  part 
going  to  the  left,  it  will  be  seen  that  after  passing  through  the 
coil  1  the  current  arrives  at  the  next  commutator  bar  to  the  right 
of  the  one  from  which  it  started.  This  bar  is  insulated  from  all 
the  other  bars  and  the  only  possible  path  for  the  current  is  through 


24        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


the  coil  2.  Passing  through  this  coil  in  the  same  way,  it  arrives 
at  the  third  commutator  bar.  As  the  current  may  continue  in  this 
way  it  is  evident  that  it  will  finally  arrive  at  the  brush  B,  and 
be  free  to  pass  out. 

In  the  same  way  the  current  passing  to  the  right  may  be  traced. 
It  will  be  found  that  each  time  the  current  passes  through  a  coil 
it  moves  one  commutator  bar  to  the  left  and  finally  arrives  at  the 
brush  Br. 

Alternate  brushes  are  connected  together  as  shown  so  that 
the  total  current  going  to  the  machine  divides  into  as  many  parts 
as  there  are  pairs  of  brushes  and,  as  stated,  each  of  these  parts 
again  divides  into  two  parts  at  the  brush.  Finally  all  the  currents 


I  I 


_ 
I  I 


L 


FIG.  16. 

come  out  again  at  the  proper  brushes  and  are  combined  into  a 
single  current  in  the  main  leads. 

If  while  tracing  through  the  windings  in  this  way  we  place 
arrows  on  the  respective  conductors  to  indicate  the  direction  of 
the  currents,  the  directions  will  be  as  shown  in  Fig.  16.  Con- 
sidering the  armature  as  a  whole, we  have  a  number  of  broad  bands 
of  current,  that  is,  all  the  individual  currents  in  each  band  are 
in  the  same  direction.  The  span  of  the  coils  and  the  positions 
of  the  brushes  are  such  that  the  width  of  each  of  these  bands  is 
just  the  width  of  a  pole  span  of  the  field,  that  is,  there  are  as 
many  bands  as  there  are  poles  in  the  field.  If  the  brushes  are 
so  placed  that  the  point  at  which  the  band  changes  direction 
comes  opposite  the  space  between  two  poles,  we  shall  have  the 


ELECTRIC  MOTORS 


25 


same  condition  as  shown  in  Figs.  9  and  11,  namely,  a  band 
or  current  lying  under  each  pole.  Each  of  these  bands  will  be 
pushed  in  the  same  direction  by  the  action  of  the  field,  and  con- 
sequently the  armature  as  a  whole  will  tend  to  rotate  or  the 
machine  will  act  as  a  motor. 

28.  The  Wave  Winding. — The  lap  winding  or  parallel  winding 
described  is  the  one  in  most  common  use,  particularly  in  large 
machines.  Many  of  the  smaller  machines  have  what  is  known 
as  a  wave  or  series  winding.  In  this  type  of  winding,  the  ends  of 
a  coil  instead  of  being  connected  to  adjacent  commutator  bars 
are  connected  to  bars  whose  distance  apart  corresponds  to  nearly 
twice  the  distance  between  two  poles.  The  connections  are 
shown  in  Fig.  17.  Starting  from  one  of  the  brushes,  say  A,  and 


FIG.  17. 


tracing  the  winding  through  to  the  brush  B,  it  will  be  found  that 
there  will  be  current  in  all  of  the  coils  (with  the  exception  of  those 
short-circuited  by  the  brushes),  even  though  we  ignore  entirely  the 
brushes  Ar  and  B'.  Consequently,  the  machine  will  operate  prop- 
erly even  though  only  twd  brushes  are  used.  In  small  machines 
it  is  customary  to  use  the  two  brushes  only.  In  larger  machines, 
where  the  current  to  be  carried  is  large,  one  brush  to  each  pole 
is  usually  employed.  In  this  way  sufficient  contact  area  between 
the  brushes  and  the  commutator  is  obtained  without  making  the 
commutator  too  long. 

In  some  classes  of  motors,  notably  those  used  on  railway  cars, 
it  is  highly  desirable  that  the  brushes  be  readily  accessible  for 
inspection  or  renewal.  With  traction  motors,  therefore,  it  is 


26        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


ELECTRIC  MOTORS  27 

customary  to  use  only  two  brushes.  They  are  placed  on  the 
upper  part  of  the  commutator  so  that  they  may  be  easily  reached 
through  the  car  floor. 

It  will  be  seen  that  some  of  the  conductors  in  Fig.  17  have  no 
arrows  placed  on  them.  The  reason  is  that  the  coils  of  which 
these  conductors  form  a  part  are  for  the  moment  short-circuited 
by  one  of  the  brushes.  The  current  is  therefore  in  the  act  of 
reversing,  and  it  would  be  difficult  to  say  what  the  direction  of 
the  current  is  at  the  instant.  While  the  lap  winding  of  Fig.  16 
shows  twenty  slots,  twenty  coils  and  twenty  commutator  bars, 
any  number  might  have  been  used.  This  will  be  readily  apparent 
if  the  reader  will  actually  construct  the  diagram,  using  say 
twenty-one  slots  and  the  corresponding  number  of  coils  and 
bars. 

29.  Number  of  Coils  in  Wave-wound  Armature. — It  is  im- 
possible,  however,  to   construct  the  wave  winding  of  Fig.    17 
with  twenty  coils,  since  the  winding  would  close  on  itself  the 
first  time  around.     We  are,  therefore,  forced  to  use  an  odd  num- 
ber and  twenty-one  was  chosen.     With  six  poles,  the  number 
might  be  either  odd  or  even,  but  it  would  have  to  be  a  number 
made  up  by  multiplying  some  integer  by  three  and  either  adding 
or  subtracting  one.     For  a  larger  number  of  poles  a  corresponding 
rule  would  hold,  namely,  the  number  of  coils  must  be  obtained  by 
multiplying  an  integer  by  half  the  number  of  poles  and  adding  or 
subtracting  one.     We  may  express  this  by  the  equation, 

N =\y± i 

where 

N  =  number  of  coils  or  commutator  bars, 
n  =  number  of  poles, 
y  =  pitch  of  winding. 

30.  Construction  of  Small  Motor. — Fig.  18  shows  the  parts  of 
a  small  motor  or  generator.     The  machine  is  of  the  four-pole 
type.     The  armature  is  slotted  and  the  coils  are  beneath  the 
surface   of   the  iron.     The  armature  is  wave  wound  and  four 
brushes  are  used.     The  bearings  are  of  the  ring-oiled  type  and 
are  supported  in  cast-iron  housings.     The  pole  pieces  are  detach- 
able so  that  a  field  coil  can  be  readily  removed  if  necessary. 


CHAPTER  III 
GENERAL    PRINCIPLES    OF    DYNAMOS    AND    MOTORS 

31.  Classification  of  Dynamos  and  Motors. — A  dynamo- 
electric  machine  is  an  apparatus  for  converting  mechanical 
energy  into  electrical  energy  or  vice  versa.  The  former  is  a 
dynamo  or  a  generator,  the  latter  is  a  motor.  This  definition 
would,  strictly  speaking,  include  static  machines,  but  these  are 
ordinarily  considered  separately. 

It  was  once  a  common  practice  to  classify  electrical  machines 
as  generators  and  motors.  However,  this  is  not  advisable 
when  considering  the  subject  in  its  broad  aspects  since  any 
electrical  machine  may  act  as  either  a  generator  or  a  motor. 
Many  machines  are  so  operated.  This  applies  even  to  such 
machines  as  the  induction  motor,  and  the  static  machine, 
although  we  do  not  frequently  use  the  former  as  a  generator  or 
the  latter  as  a  motor. 

Again,  the  classification  into  direct-  and  alternating-current 
machines  was  once  satisfactory  as  one  kind  could  always  be 
distinguished  from  the  other  by  the  presence  or  absence  of  a 
commutator.  To-day,  however,  we  have  many  alternating- 
current  motors  provided  with  commutators  and  some  direct- 
current  generators  without  commutators.  Hence  this  classifica- 
tion is  also  somewhat  unsatisfactory.  Perhaps  the  classification 
given  below  is  as  good  a  one  as  can  be  devised  at  the  present  time. 

1.  Commutating  Machines   (Generally  Continuous   Current). — 
These  machines  usually  generate  (or  use,  if  employed  as  motors) 
a  uniform  current,  that  is,  the  strength  of  the  current  does  not 
change  materially,  except  at  comparatively  long  intervals  when 
the  load  is  changed.    Some  alternating-current  machines  are  how- 
ever of  the  commutating  type. 

2.  Synchronous    Machines,    or   Alternators. — These    machines 
generate  or  consume  a  current  which  is  rapidly  changing  its 
direction,  so  that  it  flows  alternately  in  one  direction   and  in 
the  other.     The  machines  may  have  a  single  winding  generat- 
ing or  consuming  one  current,  in  which  case  they  are  called 

28 


DYNAMOS  AND  MOTORS  29 

single-phase  machines,  or  they  may  have  two  or  more  windings, 
in  which  case  they  are  called  polyphase  synchronous  machines. 

3.  Rectifying  Machines. — These  would  be   classed  by  many 
authors  with  commutating  machines.     They,  however,  generate 
primarily  an  alternating  current  either  single  phase  or  polyphase, 
and  this  is  rectified  by  means  of  a  commutator  with  few  bars. 
The  current,  therefore,  is  not  entirely  steady,  but  has  a  rapid 
pulsation  in  value,  although  it  does  not  reverse  in  direction. 
Such  machines  were  formerly  used  in  arc  lighting,  but  are  not  in 
general  use  now. 

4.  Induction  Machines. — These  differ   from  the  synchronous 
machines  principally  in  the  fact  that  the  field,  instead  of  being 
excited  by  means  of  a  direct  current,  is  excited  by  alternating 
currents.     This  gives  the  machine  the  characteristic  that  instead 
of  operating  at  constant  speed  like  a  synchronous  machine,  its 
speed  decreases  with  load  as  a  motor  and  increases  as  a  generator. 

5.  Unipolar  or  Acyclic  Machines. — These  are  machines  generat- 
ing a  continuous  current,  but  so  arranged  that  the  conductors 
revolve  at  all  times  in  a  field  of  the  same  sign.     This  avoids  the 
need  for  a  commutator. 

32.  General  Principles. — In  all  dynamos,  whether  used  as 
generators  or  as  motors,  there  are  two  principal  elements  which 
the  author  calls  the  Flux  Sheet  and  the  Current  Sheet.1  Since 
every  element  of  current  lying  in  a  magnetic  field  is  acted  upon 
by  the  field  in  such  a  manner  as  to  tend  to  force  it  across  the 
field,  it  follows  that  if  the  current  sheet  is  arranged  to  be  per- 
pendicular to  the  flux  sheet,  the  current  sheet  as  a  whole  will 
be  forced  in  the  one  direction  or  the  other  across  the  flux  sheet. 
Of  course,  the  same  force  that  is  exerted  on  the  current  sheet 
will  also  be  exerted  on  the  flux  sheet,  in  the  reverse  direction. 
Thus  either  one  or  both  may  move.  This  movement  is  generally 
a  circular  motion  about  an  axis  or  shaft.  ^The  direction  of 
motion  may  be  found  by  means  of  the  rule  of  Art.  10. 

If  the  machine  is  allowed  to  rotate  in  the  direction  in  which  the 
current  sheet  tends  to  move,  the  machine  acts  as  a  motor  and 
consumes  electrical  power.  If,  on  the  other  hand,  the  machine  is 
forced  to  rotate  in  the  opposite  direction,  it  becomes  a  generator, 
consuming  mechanical  power  and  giving  out  electrical  power. 

1  The  term  " sheet"  is  not  entirely  satisfactory  since  neither  the  flux  nor 
the  current  is  in  exactly  the  form  of  a  sheet.  The  meaning  will,  however, 
be  evident. 


30        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

In  order  that  the  torque  and  consequently  the  power  of  the 
machine  may  be  as  great  as  possible,  it  is  necessary  that  the  flux 
and  the  current  sheets  retain  the  same  relative  position.  In 
general,  there  will  be  several  flux  sheets  of  alternately  reversed 
polarity,  and  a  corresponding  number  of  current  sheets,  also  of 
alternately  reversed  direction.  Thus  Fig.  19  illustrates  the  general 
distribution  of  the  flux  and  the  current  sheets  of  a  direct-current 
motor  or  generator.  To  obtain  the  maximum  power  from  the 
machine  it  is  necessary  that  the  current  sheets  should  change 
polarity  at  approximately  half  way  between  the  flux  sheets. 
For  example,  Fig.  19  shows  that  all  the  conductors  between  the 
lines  A  and  B  should  carry  current  in  the  same  direction,  if  the 
maximum  torque  is  to  be  developed,  since  all  lie  in  a  magnetic 
field  of  the  same  sign.  If  the  current  in  some  of  them  were 


FIG.  19. 

reversed,  the  pull  of  those  conductors  would  be  exerted  in  the 
reverse  direction  to  that  of  the  others,  and  the  output  of  the 
machine  as  a  motor  would  be  decreased.  It  would  likewise  be 
decreased  if  the  machine  were  operating  as  a  generator,  since  it 
will  be  apparent  that  the  e.m.f.  induced  in  all  of  the  conductors 
from  A  to  B  will  be  in  the  same  direction.  For  action  as  a 
generator  the  current  must  flow  in  the  same  direction  as  the 
induced  e.m.f.  Consequently,  the  current  should  be  in  the  same 
direction  in  all  of  the  conductors. 

The  arrangement  of  the  flux  sheets  and  the  current  sheets 
shown  in  Fig.  19  is  that  of  a  direct-current  generator  or  motor, 
The  same  arrangement  in  its  essential  features  is  common  to  a 
great  variety  of  electrical  machines.  In  fact,  all  machines  both 
direct  and  alternating  current,  with  the  exception  of  the  unipolar 
machine,  employ  essentially  this  arrangement.  The  principal 


DYNAMOS  AND  MOTORS  31 

difference  between  the  various  types  of  machines  comes  from  the 
different  arrangements  necessary  to  obtain  this  distribution. 

Coming  back  to  the  case  of  the  continuous- current  machine, 
as  shown  in  Fig.  19  it  will  be  seen  that  the  flux  is  produced  by  a 
number  of  poles.  The  flux  passes  through  each  of  the  cores 
and  divides  into  two  equal  parts  in  the  armature  and  also  in 
the  yoke  of  the  field.  Any  even  number  of  poles  may  be  em- 
ployed. However,  machines  are  rarely  built  with  less  than 
four  poles  except  in  the  smallest  sizes. 

To  produce  this  flux,  each  pole  is  surrounded  by  a  coil  of  wire. 
The  different  coils  are  usually  connected  all  in  series,  although 
other  groupings  may  be  used  if  more  convenient.  It  is  also 
common  to  employ  two  coils  per  pole,  in  order  to  improve  the 
action  of  the  machine  in  certain  respects.  The  current  for  the 
coils  may  be  supplied  in  various  ways  as  will  be  described  later. 

33.  Commutators. — With  a  distribution  of  the  flux  in  bands  of 
alternately  opposite  direction,  it  will  be  obvious  that  we  may  pro- 
duce a  current  sheet,  stationary  with  respect  to  the  flux  sheet  by 
passing  alternating  currents  into  the  armature,  care  being  taken  to 
operate  the  machine  at  such  a  speed,  that  the  current  reverses  in 
each  conductor  once  for  each  field  pole  passed.  The  most  advan- 
tageous position  in  which  to  reverse  the  current  is  when  each 
conductor  is  in  a  position  midway  between  the  field  poles.  The 
best  means  for  effecting  this  will  be  gone  into  later  in  connection 
with  the  synchronous  machine. 

In  the  direct-current  machine,  however,  with  the  indicated 
distribution  of  the  flux,  it  is  necessary  to  use  a  commutator. 
Resting  on  the  commutator  are  the  brushes.  These  are  usually 
of  carbon  or  graphite,  but  in  low- voltage  machines,  are  some- 
times composed  of  a  mixture  of  ground  copper  and  graphite. 
Usually,  as  many  brushes  or  sets  of  brushes  are  used  as  there  are 
field  poles,  although  a  smaller  number  are  used  for  certain 
classes  of  windings. 

Two  of  the  simplest  methods  of  connecting  the  conductors  to 
the  commutator  bars  have  been  shown  in  Figs.  16  and  17.  Each 
coil  may  consist  of  a  single  turn  or  there  may  be  several  turns  per 
coil. 

If  the  two  main  conductors  marked  +  and  —  are  connected 
to  a  source  of  continuous  current  of  corresponding  polarity, 
current  will  flow  into  all  of  the  brushes  marked  +  and  will  flow 
out  of  all  of  those  marked  -  .  By  tracing  through  the  connec- 


32        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

tions  it  will  be  evident  that  the  direction  of  the  currents  in  the 
individual  conductors  will  be  as  shown  in  Figs.  16  and  17.  The 
current  will  then  be  distributed  in  a  series  of  bands,  each  band 
comprising  ten  conductors  in  the  example  shown.  In  practice 
there  are  always  many  more  conductors  in  a  band  than  this 
number.  As  the  armature  revolves,  since  the  brushes  are  station- 
ary, the  bands  of  current  will  also  be  stationary.  The  current  in 
the  individual  conductors  will,  however,  not  be  constant,  but 
will  reverse  in  direction  each  time  that  the  commutator  bar 
connected  to  a  conductor  passes  under  a  brush. 

If  an  armature  of  this  type  be  placed  in  a  magnetic  field  as 
shown  in  Fig.  19,  and  if  the  brushes  are  in  such  a  relation  to  the 
field  structure  that  the  points  at  which  the  current  sheet  changes 
sign  are  approximately  midway  between  the  poles,  it  will  exert  a 
torque  and  if  not  restrained  will  turn  continuously  in  the  one 
direction  or  the  other,  operating  as  a  motor.  The  torque  devel- 
oped will  be  in  proportion  to  the  strength  of  the  current  in 
the  armature  and  to  the  strength  of  the  magnetic  field. 

34.  Action  as  a  Generator. — If  instead  of  being  supplied  with 
current  from  some  outside  source  and  acting  as  a  motor,  the 
machine  be  rotated  by  power  applied  through  the  shaft,  it  will 
automatically  become  a  generator  capable  of  supplying  power 
to  an  external  circuit.  Figure  19  shows  that  all  of  the  conductors 
in  the  band  between  the  points  A  and  B  are  cutting  the  flux  from 
the  pole  N  in  the  same  direction  and  consequently  all  of  them  will 
generate  an  e.m.f.  in  the  same  direction.  The  strength  of  the 
induced  e.m.f.  will  be  somewhat  different  in  the  different  con- 
ductors, and  in  fact  will  be  nearly  zero  in  those  near  the  points 
A  and  B  but  all  the  e.m.fs.  in  the  band  will  be  in  the  same 
direction.  All  of  these  conductors  are  connected  in  series  with 
one  another  and  are  connected  to  the  external  circuit  through  the 
brushes.  Figures  16  and  17  show  that  starting  from  any  one  of 
the  brushes  and  tracing  through  the  winding  to  the  next  brush, 
all  of  the  e.m.fs.  will  be  acting  in  the  same  direction.  All  of 
them  will  therefore  add  together  giving  a  terminal  e.m.f.  equal 
to  the  sum  of  their  individual  values.  No  matter  which  path  is 
selected,  the  number  of  conductors  in  series  is  the  same.  Conse- 
quently the  e.m.f.  generated  will  be  the  same  in  all  of  them,  pro- 
vided the  field  poles  are  of  equal  strength. 

It  will,  moreover,  be  noticed  that  starting  from  any  brush,  there 
are  two  possible  paths.  No  matter  which  of  those  are  chosen, 


DYNAMOS  AND  MOTORS  33 

an  e.m.f.  will  be  encountered  in  the  same  direction.  All  of  the 
paths  are  in  parallel,  and  since  their  e.m.fs.  are  the  same,  the 
action  is  similar  to  that  of  a  corresponding  number  of  primary  or 
storage  cells  connected  in  parallel.  The  external  voltage  is  that 
of  one  path  only.  The  effect  of  the  additional  paths  is  to  reduce 
the  resistance  of  the  armature.  The  current- carry  ing  capacity  is 
therefore  in  proportion  to  the  number  of  these  paths. 

If  when  such  a  machine  is  in  action,  the  terminals  +  and  — 
are  connected  through  a  suitable  resistor,  a  current  will  flow  and 
the  machine  will  act  as  a  generator,  changing  mechanical  power 
into  electrical  power.  As  soon  as  the  current  passes,  there  is, 
as  in  the  case  of  the  motor,  a  torque  between  the  armature  and 
the  field.  As  before,  this  torque  will  be  in  proportion  to  the 
strength  of  the  current  and  to  the  strength  of  the  magnetic  field. 
The  engine  or  other  prime  mover  is  therefore  required  to  exert  a 
greater  torque  as  the  current  increases,  and  in  consequence  re- 
quires an  increased  supply  of  steam,  gas,  water,  etc. 

35.  Back  E.M.F. — Referring  again  to  the  direct-current 
motor,  it  will  be  recalled  that  nothing  was  said  about  the 
e.m.f.  It  is  apparent  that  in  both  the  motor  and  generator,  the 
conductors  will  cut  the  field  flux,  and  consequently  will  generate 
an  e.m.f.  In  the  generator,  the  flow  of  current  is  in  the  same 
direction  as  the  e.m.f.,  since  it  flows  because  of  the  generated 
e.m.f.  In  the  motor,  however,  the  current  and  the  e.m.f.  are  in 
opposite  directions,  since  the  current  must  be  reversed  to  give 
torque  in  the  direction  of  motion. 

The  back  e.m.f.  in  a  motor  therefore  tends  to  cut  down  the 
current  passing  into  the  motor. 

This  phenomenon  can  be  readily  observed  by  connecting  in 
series  a  small  motor,  a  few  cells  of  battery  and  an  ammeter.  If 
the  motor  be  prevented  from  rotating,  the  current  may  be  25 
amp.  As  soon  as  the  motor  is  released  and  starts  to  rotate, 
the  current  will  decrease,  and  if  the  motor  is  allowed  to  run 
without  load,  the  current  may  drop  to  5  amp.  When  this  fact 
was  first  discovered,  it  was  considered  that  it  was  very  un- 
fortunate since  it  apparently  seriously  limited  the  power  of  the 
motor.  It  is  now  known  that  the  production  of  this  back  e.m.f. 
is  absolutely  essential  to  the  working  of  the  motor.  The  output 
of  the  machine  is,  in  fact,  proportional  to  the  value  of  the  back 
e.m.f.  and  without  it  no  power  would  be  developed.  Neglecting 
certain  other  losses  the  efficiency  of  the  motor  is  the  quotient 


34        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

of  the  back  e.m.f.  divided  by  the  applied  e.m.f.  Therefore,  in 
order  that  the  efficiency  of  the  machine  may  be  high,  it  is 
essential  that  the  back  e.m.f.  of  the  motor  be  nearly  equal  to  the 
applied  voltage.  The  current  that  flows  is  then  only  a  small 
fraction  of  that  which  would  flow  if  the  motor  were  at  rest  and 
the  same  e.m.f.  were  applied.  Hence  the  motor  develops  nor- 
mally only  a  small  percentage  of  its  maximum  torque. 

36.  Calculation  of  E.M.F.  —  The  most  important  equation 
of  the  continuous-  current  generator  or  motor  is  that  con- 
necting the  generated  e.m.f.  with  the  flux,  the  speed,  the 
number  of  poles  and  the  number  of  conductors  on  the  armature. 
The  calculation  may  be  made  very  readily  without  the  use  of  a 
formula.  Assume  a  six-pole  generator  operating  at  a  speed  of 
600  r.p.m.  Let  the  flux  per  pole  be  1,000,000  lines  and  assume 
the  total  number  of  conductors  on  the  armature  to  be  840.  The 
armature  is  supposed  to  have  a  two-path  wave  winding  as  shown 
in  Fig.  17.  The  e.m.f.  generated  is  simply  the  number  of  lines 
cut  in  a  second,  divided  by  108.  In  one  revolution  one  con- 
ductor will  cut  6,000,000  lines  and  in  1  sec.  it  will  cut 
60,000,000  lines.  In  a  two-path  wave  winding  half  the  con- 
ductors are  in  series  and  the  total  cutting  per  second  is  therefore 
420  times  as  great  or  252  X  108.  This  is  the  generated  e.m.f. 
in  absolute  units,  or  the  machine  is  generating  252  volts. 

If  the  armature  had  been  lap  wound,  as  shown  in  Fig.  16,  the 
number  of  paths  through  it  would  have  been  six  instead  of  two  or 
we  should  have  had  140  conductors  in  series.  The  generated 
voltage  would  have  been  one-third  as  great  or  84  volts.  It 
should  be  carefully  noted  that  in  this  case  the  armature  would 
have  been  capable  of  carrying  three  times  as  much  current  as  it 
could  carry  wave  wound,  or  the  capacity  of  the  machine  would  be 
the  same  in  the  two  cases. 

The  foregoing  facts  can  be  readily  expressed  by  means  of  a 
formula.  Let  3>  be  the  flux  per  pole,  n  the  number  of  revolutions 
per  second,  Nr  the  total  number  of  conductors  on  the  armature, 
P  the  number  of  poles  and  P'  the  number  of  paths  through  the 
winding.  The  number  of  conductors  in  series  is  Nf  •*•  P',  the 

N'&P 
cutting  per  revolution,      „,    ,  and  the  generated  e.m.f.  is  given 

QN'nP 
by  the  formula  E  =         p/  •     For  simplicity  we  shall  frequently 


N'P 

substitute  N  =  -pr,  in  the  above  and  write  E  =  -TQT"«     Fre- 


DYNAMOS  AND  MOTORS 


35 


quently  the  number  of  paths  is  the  same  as  the  number  of  poles 
and  in  this  case  P  =  Pf. 

37.  Methods  of  Field  Excitation. — The  Magneto  Machine 
and  the  Separately  Excited  Machine. — The  most  obvious  method 
of  constructing  a  motor  or  generator  is  with  a  permanent  magnet 
for  the  field.  The  chief  objection  to  this  is  the  high  cost  of  the 
steel  used  in  such  magnets.  This  alone  would  make  the  cost 
of  a  machine  of  reasonable  size  prohibitive.  In  addition,  it 
would  be  impossible  to  produce  in  this  manner  machines  with 
as  strong  fields  as  are  now  considered  advisable.  The  output 
for  a  given  size  would  therefore  be  low  and  the  cost  per  kilowatt 
correspondingly  high.  It  would  also  be  difficult  to  provide 
proper  means  for  varying  the  voltage  of  such  a  machine,  since 
the  strength  of  the  field  could  not  readily  be  changed.  These 


Battery 

WWW 

Field    Kheo8tat 


FIG.  20. 


objections  have  such  weight  that  permanent  magnets  are  never 
used,  except  in  the  case  of  small  generators  used  for  ringing 
telephone  bells,  or  for  the  ignition  of  internal  combustion  engines. 
In  these  cases,  the  fact  that  the  field  is  always  present  and  is 
independent  of  the  speed,  is  of  more  importance  than  the  low 
ouput  and  high  cost  of  such  machines. 

Figure  20  shows  a  separately  excited  machine.  The  source  of 
current  for  the  field  may  be  a  battery,  a  small  generator  supplied 
for  this  purpose  or  other  source  of  continuous  current.  The 
brushes  as  shown  are  placed  90°  from  the  position  indicated  in 
Fig.  9,  which  had  reference  to  a  ring-wound  armature.  Separate 
field  excitation  is  almost  universal  in  the  case  of  synchronous 
machines,  since  on  account  of  the  alternating  character  of  the 
current  generated,  it  is  necessary  to  provide  some  other  source 


36        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


of  direct  current  than  the  machine  itself.  It  is  but  rarely 
employed  in  continuous-current  machines,  and  then  generally  in 
connection  with  some  special  method  of  regulation. 

In  most  continuous- current  machines,  the  machine  generates 
the  current  to  excite  its  fields,  or  if  a  motor,  takes  the  field  current 
from  the  same  circuit  as  that  for  the  armature.  While  it  appears 
to  be  almost  obvious  that  this  may  be  done,  the  early  builders  of 
dynamos  were  very  slow  to  appreciate  this  possibility  and  dynamo 
machines  went  through  a  long  evolution  before  they  were 
generally  so  built. 

38.  The  Shunt-wound  Machine. — The  field  coils  of  self- 
exciting  dynamos  may  be  connected  in  one  of  the  three  methods 
shown  in  Figs.  21,  22,  and  23.  The  first  method  is  known  as  the 
shunt  connection.  The  current  supplied  to  the  field  will  be  equal 


FIG.  21. 


FIG.  22. 


to  the  terminal  e.m.f .  of  the  machine  divided  by  the  resistance  of 
the  field  circuit.  If  the  terminal  voltage  of  the  machine  is 
constant,  the  current  through  the  shunt  winding  will  be  constant, 
and  consequently  the  magnetic  flux  passing  through  the  field  and 
armature  will  also  be  constant.  This  type  of  winding  is  there- 
fore particularly  applicable  to  machines  intended  to  deliver  a 
substantially  constant  voltage. 

When  a  shunt  dynamo  is  at  rest,  there  is  of  course  no  current  in 
either  the  field  or  armature  windings.  When  the  armature 
is  rotated  there  is  generated  in  it  a  feeble  e.m.f.  due  to  the  fact 
that  some  residual  magnetism  is  left  in  the  field.  This  small 
e.m.f.  causes  a  current  to  flow  through  the  field  winding.  This 
in  turn  increases  the  field,  thus  again  increasing  the  e.m.f. 
This  action  continues  until  the  field  reaches  a  certain  point  of 
saturation.  This  action  is  called  "building  up." 


DYNAMOS  AND  MOTORS 


37 


39.  The  Series-wound  Machine. — In  series-wound  machines 
(see  Fig.  22),  the  whole  current  generated  by  the  machine  passes 
through  a  few  turns  of  comparatively  coarse   wire.     The  field 
current   is   therefore    proportional   to   the    current   which    the 
machine  is  generating.     The  field  flux  will  increase  as  the  current 
output  of  the  machine  increases  although  not  so  rapidly  as  the 
latter  on  account  of  magnetic  saturation.     Hence  the  voltage  of 
such  a  machine  will  increase  as  the  load  on  the    machine  is 
increased. 

40.  The  Compound  Wound  Machine. — The  compound  winding 
shown  in  Fig.  23  employs  a  combination  of  the  shunt  and  the 
series  windings.     In  general  the  series  turns  are  so  connected 
that  they  help  the  shunt  turns.     The  machine  will,  therefore, 


FIG.  23. 


have  intermediate  characteristics,  and  will  generally  increase 
somewhat  in  voltage  as  the  load  is  increased.  The  exact  effect 
of  these  windings  is  treated  in  more  detail  later. 

41.  Magnetic  Effect  of  the  Armature. — Before  considering 
more  fully  the  voltage  regulation  of  direct-current  machines  and 
the  speed  regulation  of  motors,  it  is  necessary  to  investigate 
the  magnetizing  effect  of  the  armature  as  well  as  that  of  the  field 
winding.  In  general,  it  may  be  said  that  all  of  the  current 
passing  through  a  machine  has  a  part  in  setting  up  the  magnetiza- 
tion. In  a  continuous-current  machine,  the  arrangement  is 
purposely  such  that  the  magnetizing  effect  of  the  armature  is  a 
minimum.  In  other  types  of  machines,  as  the  synchronous 
machines,  its  effect  may  in  many  cases  be  very  great,  and  in  the 
induction  motor,  the  effective  magnetizing  effect  is  due  to  the 


38        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

difference  between  that  of  the  stator  (armature)  and  that  of  the 
rotor  (field),  so  that  the  former  is  always  the  greater. 

Figure  24  shows  a  section  of  a  continuous-current  machine. 
For  simplicity  the  machine  represented  is  bipolar.  The  path  of 
the  magnetic  lines  is  approximately  as  shown.  It  will  be  seen 
that  not  all  of  the  lines  which  pass  through  the  field  pass  through 
the  armature  also.  In  order  to  force  the  lines  across  the  air  gap, 
it  is  necessary  that  a  large  portion  of  the  magnetizing  effect  of 
the  machine  be  concentrated  at  the  air  gap.  On  this  account, 
and  on  account  of  the  crowding  of  the  lines  of  induction,  some  of 
the  lines  find  it  easier  to  take  the  path  shown  from  pole  to  pole 
without  going  through  the  armature  at  all.  In  general,  from 
10  to  20  per  cent,  more  lines  will  pass  through  the  fields  than 
through  the  armature. 

Considering  Fig.  24  again  and  neglecting  the  effect  of  magnetic 
leakage,  the  magnetizing  effect  of  a  certain  number  of  ampere 
turns  upon  the  magnetic  circuit  is  the  same  no  matter  where  the 
turns  are  placed.  The  most  common  location  is  at  the  points  A 
and  C  the  coil  being  divided  into  two  equal  parts,  and  half 
placed  on  each  side.  It  is,  however,  entirely  possible  to  use 
only  one  coil  located  at  B,  and  many  bipolar  dynamos  are  so 
constructed.  In  multipolar  machines,  this  location  leads  to  great 
mechanical  difficulties  and  is  not  used. 

It  would  also  be  entirely  possible  to  make  use  of  a  stationary 
coil  slightly  larger  than  the  armature  and  located  at  the  point  D 
(so  as  to  surround  the  armature).  This  is  occasionally  though 
rarely  done. 

42.  Armature  Reaction. — It  is  apparent  that  a  turn  located  on 
the  armature  itself  in  the  position  D  will  have  the  same  magnetiz- 
ing effect  while  it  is  in  the  position  shown  as  though  it  were 
stationary.  This  fact  is  at  the  bottom  of  the  idea  of  armature 
reaction.  In  the  actual  machine,  the  turns  are  located  as  shown 
in  Fig.  25.  The  dots  represent  currents  coming  toward  the 
observer ;  the  crosses,  currents  flowing  from  him.  The  angle  which 
the  line  AB  makes  with  the  vertical,  depends  upon  the  position 
of  the  brushes.  When  the  brushes  are  in  such  a  position  as  to 
give  the  distribution  shown,  they  are  said  to  be  in  the  neutral 
position,  and  the  magnetizing  effect  of  the  armature  upon  the 
field  is  nearly  zero.  Thus  considering  any  particular  conductor 
as  C  there  will  be  another  conductor  D  symmetrically  located 


DYNAMOS  AND  MOTORS 


39 


upon  the  armature,  and  carrying  current  in  the  opposite  direction. 
Therefore  the  net  effect  of  the  two  conductors  will  be  nearly  zero. 

If,  on  the  other  hand,  the  brushes  in  Fig.  25  had  been  rocked 
90°  from  the  neutral  position,  the  armature  would  have  had  its 
maximum  magnetizing  effect.  Instead  of  being  able  to  find  for 
each  conductor  another  conductor  which  would  offset  its  action, 
we  should  be  able  to  find  for  each  conductor  another  so  located 
as  to  help  the  magnetizing  action  of  the  first.  Consequently, 
with  the  brushes  in  this  position,  the  armature  would  have  a 
powerful  effect  upon  the  magnetization  of  the  machine. 

Figure  26  shows  the  conditions  in  a  machine  in  which  the 
brushes  are  rocked  a  moderate  distance  from  the  neutral  axis. 


This  corresponds  to  the  general  case  in  practice.  The  slight 
rocking  of  the  brushes  is  to  assist  commutation,  as  will  be  ex- 
plained later.  It  will  be  readily  seen  that  taking  the  conductors 
from  A  to  D  and  those  from  B  to  C  the  magnetizing  effect  of  the 
one  band  will  be  exactly  offset  by  that  of  the  other,  and  the  net 
effect  will  consequently  be  zero.  The  conductors  in  the  bands  A 
to  B  and  C  to  D,  however,  are  so  situated  that  they  assist  one 
another,  either  to  increase  or  to  decrease  the  total  magnetization 
of  the  machine.  In  a  machine  acting  as  a  generator,  it  is  neces- 
sary to  rock  the  brushes  forward  of  the  neutral  position  in  order 
to  secure  the  best  results  in  commutation.  In  this  position  the 
currents  in  the  bands  AB  and  CD  are  in  such  a  direction  as  to 
tend  to  demagnetize  the  field,  and  the  flux  is  thus  weakened.  In 


40        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

a  motor,  it  is  necessary  to  rock  the  brushes  backward.  This 
would  reverse  the  direction  of  the  current  in  the  bands,  but  in 
addition  the  current  is  reversed  since  the  machine  is  acting  as  a 
motor.  The  net  consequence  is  that  the  magnetizing  effect  of 
the  bands  is  in  the  same  direction  as  before,  or  they  still  tend  to 
demagnetize  the  field. 

PROBLEMS 

12.  In  a  dynamo  the  flux  passes  in  succession  through  two  air  gaps  each 
}$  in.  long,  section  100  sq.  in.;  an  armature  in  which  the  mean  path  is  8  in., 
section  80  sq.  in.,  permeability  500;  two  field  cores  each  7  in.  long,  section 
60  sq.  in.,  permeability  350;  and  a  cast-iron  yoke  9  in.  long,  section  120  sq. 
in.,  permeability   180.     Assuming  that  the  total  flux  is  the  same  in  all 
parts  of  the  machine,  how  many  ampere  turns  are  required  in  order  that 
there  may  be  50,000  lines  per  square  inch  in  the  air  gap?     If  there  are  2000 
turns  on  the  field,  what  is  the  current  needed  to  obtain  the  above  flux 
density  ? 

13.  A  certain  armature  is  10  in.  long.     The  flux  density  is  40,000  lines 
per  square  inch.     What  is  the  e.m.f.  generated  in  one  conductor  moving  at 
the  rate  of  4000  ft.  per  minute?     If  the  pole  shoes  cover  70  per  cent,  of  the 
armature  surface  what  is  the  average  voltage  during  a  complete  revolution? 

14.  A  certain  armature  is  15  in.  long  and  25  in.  in  diameter.     In  order 
that  sparking  may  be  avoided  it  is  necessary  that  there  be  generated  in  each 
conductor  under  the  commutating  pole  2  volts.     What  is  the  necessary  flux 
density  if  the  machine  is  rotating  at  the  rate  of  900  r.p.m.  and  if  the  interpole 
is  iy%  in.  long,  measured  parallel  to  the  shaft? 

15.  A  rod  of  copper  is  falling  vertically  at  the  rate  of  100  ft.  per  minute. 
The  horizontal  component  of  the  magnetic  field  of  the  earth  is  0.029  lines 
per  square  inch.     If  the  rod  is  10  ft.  long  and  is  pointing  due  east  and  west 
as  it  falls,  what  is  the  voltage  between  the  ends  of  the  rod? 

16.  A  certain  six-pole  direct-current  generator  has  an  armature  43  in.  in 
diameter  by  10  in.  long.     Each  pole  shoe  is  10  in.  by  12^  in.     There  are 
534  conductors  on  the  armature.     There  are  two  paths  through  the  arma- 
ture, so  that  half  of  the  conductors  are  in  series.     If  the  density  in  the  air 
gap  is  56,000  lines  per  square  inch,  what  must  the  speed  be  in  order  that  the 
machine  may  generate  250  volts? 

17.  Each  conductor  on  the  foregoing  machine  carries  a  current  of  200 
amp.     What  is  the  force  in  dynes  acting  on  a  conductor  under  the  pole  face? 
In  pounds?     What  on  one  not  under  the  pole  face?     What  is  the  force  in 
pounds  acting  on  the  whole  armature,  taking  account  of  the  fact  that  not 
all  of  the  conductors  are  under  the  pole  faces? 

18.  What  would  be  the  power  output  of  the  foregoing  dynamo  if  none 
of  the  voltage  generated  were  lost?     What  is  the  horse  power  required  to 
keep  it  in  motion,  using  the  answer  to  the  above  problem  and  assuming  that 
the  friction,  etc.,  is  zero?     How  many  kilowatts  are  required?     Does  this 
correspond  with  the  power  output?     Would  this  result  be  obtained  in 
practice? 


CHAPTER  IV 
SYSTEMS  OF  DISTRIBUTION 

43.  The  Constant  Current  System. — Before  taking  up  the 
subject  of  the  regulation  of  dynamo  machines,  it  is  necessary 
to  consider  briefly  the  methods  of  distributing  and  utilizing  the 
electric  current.  In  the  earliest  electric  generators,  the  machines 
were,  in  general,  used  to  supply  current  to  one  device  only.  Thus, 
a  certain  generator  might  supply  current  for  an  arc  light,  and  for 
no  other  purpose.  The  voltage  would  be  regulated  to  the  proper 
value,  and  no  further  regulation  would  be  required. 

As  the  use  of  electricity  increased,  however,  it  soon  became 
apparent  that  it  would  be  necessary  to  provide  means  whereby  a 
great  number  of  devices  might  be  operated  independently  of 
one  another  from  one  generator.  Thus  at  the  present  time  it- 
is  not  uncommon  to  find  thousands  of  incandescent  lamps, 
numerous  arc  lights,  electric  railway  systems,  electrified  sections 
of  main  line  railways,  electrical  heaters,  thousands  of  horse  power 
in  electric  motors,  besides  numerous  other  devices,  all  operated 
from  the  same  power  house,  and  taking  current  from  the  same 
generators. 

Perhaps  the  simplest  method  of  distribution  is  illustrated  in 
Fig.  27  which  shows  the  connections  of  the  series  or  constant  cur- 
rent system.  The  various  devices  are  connected  as  shown  so 
that  the  same  current  passes  through  all  of  them  in  series.  Neg- 
lecting a  possible  slight  leakage,  the  current  is,  of  course,  the 
same  in  all  parts  of  the  circuit.  In  order  that  it  should  be  possible 
to  operate  any  number  of  the  devices  separately  or  in  any  combina- 
tion, it  is  necessary  that  the  dynamo  be  so  constructed  that  its 
current  remains  constant  at  all  times.  The  voltage  generated 
must  vary  in  proportion  to  the  load  connected  in  the  circuit  at 
any  time.  Thus  with  two  incandescent  lamps,  three  arc  lamps 
and  a  motor  connected  as  shown  in  Fig.  27,  and  requiring  the 
voltages  shown  to  force  the  current  through  them,  we  should  have 
to  generate  a  voltage  equal  to  the  sum  of  the  individual  voltages 

41 


42        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

or  270  volts  plus  enough  voltage  to  overcome  the  El  drop  in 
the  line.  To  cut  out  one  of  the  devices  the  corresponding  switch 
would  be  closed,  thus  providing  a  short  circuit  around  the  de- 
vice, and  causing  the  current  to  take  this  path  instead  of  that 
through  the  lamp  or  motor.  In  order  that  the  current  may  re- 
main constant  it  is  therefore  necessary  that  the  voltage  should 
decrease  as  lamps  are  turned  off. 

There  are  various  vital  objections  to  this  scheme.  At  present 
it  is  used  only  in  certain  special  cases,  for  example,  the  operation 
of  street  lights.  These  are,  as  a  rule  operated  upon  alternating- 
current  circuits,  and  even  in  this  case,  the  regulation  required  is 
obtained  from  a  special  transformer  and  not  from  the  generator. 

The  principal  objection  to  this  method  of  distribution  will  be 
apparent  if  we  consider  a  typical  case.  The  highest  current  that 


FIG.  27. 

it  is  considered  commercially  practicable  to  use  with  arc  or  in- 
candescent lamps  is  about  10  amp.  Many  arc  lamps  require 
about  500  watts,  or  10  amp.  at  50  volts.  An  incandescent  lamp 
of  moderate  size  would  require  10  amp.  at  5  volts  or  50  watts. 
With  a  voltage  at  the  dynamo  of  6000  volts  we  should  therefore 
be  able  to  operate  120  arc  lamps  or  1200  incandescent  lamps  of  the 
size  mentioned.  The  power  expended  in  the  circuit  would  be 
10  X  6000  =  60,000  watts  or  60  kw.  Since  a  horse  power  is 
equal  to  0.746  kw.,  this  would  be  equal  to  80  hp. 

It  would  not  be  practicable  to  increase  the  voltage  above  this 
figure  since  this  is  already  higher  than  the  maximum  allowed  by 
the  municipal  regulations  of  most  cities.  Neither  is  it  practicable 
to  increase  the  current  beyond  the  figure  given.  Even  at  the 
voltage  mentioned,  the  impossibility  of  attempting  to  pass  the 
current  into  homes  for  general  use  will  be  apparent. 


SYSTEMS  OF  DISTRIBUTION 


43 


We  should  thus  be  limited  to  about  60  kw.  or  80  hp.  on  each 
circuit  and  consequently  to  generators  of  a  corresponding  size. 
Such  dynamos  would  be  mere  pigmies  in  comparison  with  the 
machines  in  modern  power  houses,  where  generators  of  1000 
kw^are  very  common  and  units  of  from  10,000  to  35,000  kw.  are 
not  unusual.  Motors  adapted  to  work  on  a  constant  current 
are  also  very  unsatisfactory.  Without  further  multiplying 
reasons,  it  will  be  apparent  that  such  constant  current  distribu- 
tion would  be  totally  unsuitable  for  use  in  a  modern  system  of 
electrical  supply. 

44.  The  Constant  Potential  System. — In  modern  installations, 
practically  all  of  the  power  is  distributed  at  constant  potential. 


Arc  Lights 


The  general  arrangement  of  such  a  system  is  illustrated  in  Fig. 
28.  All  the  receiving  elements  are  " bridged"  across  the  line  as 
shown.  It  is  evident  that  if  the  difference  of  potential  across  the 
lines  remains  the  same  at  all  times  and  all  places,  any  one  of  the 
receiving  units  maybe  connected  or  disconnected  without  in  any 
way  affecting  the  remainder. 

The  conditions  in  such  a  system  will  be  more  clearly  under- 
stood from  the  simpler  diagram  of  Fig.  29.  The  generator  is 
supposed  to  furnish  current  at  a  uniform  pressure  of  110  volts. 
If  no  lamps  are  turned  on,  the  current  will  be  zero,  the  voltage 
110.  Suppose  that  all  of  the  lamps  have  the  same  resistance, 
110  ohms.  If  one  lamp  such  as  A  be  turned  on  the  current  pass- 
ing through  it  will  be  I  =  E/R  =  110/110  =  1  amp.  This  same 


44        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

current  will  flow  through  the  generator,  and  if  the  lamp  is  adapted 
to  this  current,  it  will  be  properly  lighted.  If  now  another  lamp 
be  switched  on,  it  also  will  take  a  current  of  1  amp.  and  the  genera- 
tor will  supply  a  current  of  2  amp.  It  will  be  evident  that  either 
of  the  lamps  may  be  turned  on  or  off  without  any  effect  on  the 
other. 

The  conditions  when  all  four  of  the  lamps  are  turned  on  is 
shown  in  the  figure.  The  total  current  will  be  4  amp.  All  of 
this  current  will  flow  in  the  section  of  the  wire  nearest  to  the 
generator.  The  next  section  will  have  only  3  amp.  in  it,  and  so 
on. 

A  little  consideration  will  show  that  the  assumed  condition, 
namely,  that  the  difference  of  potential  between  the  wires 
is  everywhere  the  same,  can  never  be  rigorously  fulfilled.  The 
conductors  forming  the  mains  must  have  some  resistance,  and 
this  resistance  will  cause  a  drop  of  potential.  Thus  if  the  re- 


a\\A      b\\A      c\\A     d\\A 


4A   -< ZA  2A  \A 

FlG.   29. 

sistance  in  both  of  the  wires  connecting  the  first  and  the  second 
lamps  is  0.1  ohm,  there  will  be  a  drop  in  voltage  of  E=  RI  = 
3  X  0.1  =  0.3  volts.  Then  if  the  voltage  across  lamp  A  is  110, 
that  across  B  will  be  109.7  volts.  In  a  similar  way,  it  could  be 
shown  that  the  "drop"  between  B  and  C  is  0.2  volt,  and  be- 
tween C  and  D  0.1  volt.  Thus  the  voltage  applied  to  D  is  110 
minus  all  of  these  drops  or  109.4  volts.  The  above  is  not  quite 
exact,  as  we  have  neglected  the  fact  that  owing  to  the  drop  be- 
tween the  successive  lamps,  the  currents  in  all  the  lamps  except 
A  would  be  slightly  less  than  1  amp.  However,  the  computation 
is  close  enough  for  all  practical  purposes. 

By  using  larger  wire  in  the  circuit,  the  drop  between  the  lamps 
could  have  been  made  less.  At  the  same  time,  the  loss  of  power 
in  the  circuit  would  have  been  reduced.  No  matter  how  large 
the  wire,  there  would,  however,  be  some  drop  and  some  loss  of 
power.  Both  of  these  can,  however,  be  brought  within  com- 
mercial limits  without  a  prohibitive  expense  for  conductors. 


SYSTEMS  OF  DISTRIBUTION  45 

The  exact  size  of  the  wire  to  be  used  in  any  given  case  is  fre- 
quently determined  by  the  relative  interest  and  depreciation  on 
the  cost  of  the  copper,  and  the  value  of  the  power  wasted.  Some- 
times, the  deciding  feature  is  the  allowable  drop  that  may  be 
present  without  interfering  seriously  with  the  regulation  of  the 
lights,  and  frequently  the  size  is  determined  by  the  fact  that  the 
wire  must  be  large  enough  to  carry  the  current  without  undue 
heating,  which,  if  present,  would  lead  to  a  serious  fire  risk. 

45.  Regulation  of  Generators. — As  shown  in  the  preceding 
pages,  it  is  necessary  that  a  generator  be  constructed  to  hold  its 
voltage  or  its  current  constant.     The  former  requirement  is  the 
more  common  and  will  demand  more  study. 

At  an  early  period  in  the  development  of  electrical  engineering, 
particularly  while  the  const  ant- current  system  was  in  vogue, 
frequent  attempts  were  made  to  govern  the  current  or  the  voltage 
of  the  generator  by  changing  the  speed  of  the  prime  mover. 
Thus  a  solenoid  might  be  employed  connected  in  series  with  the 
circuit  in  a  constant-current  system  or  in  shunt  with  it  in  a 
constant-potential  system,  and  so  connected  with  the  governing 
mechanism  of  the  prime  mover  as  to  increase  the  speed  when  the 
current  or  the  voltage  dropped  below  the  specified  value. 
Several  facts  have  combined  to  cause  this  practice  to  fall  into 
disrepute.  In  the  first  place,  it  will  appear  from  what  follows  that 
it  is  a  simple  matter  to  construct  a  generator  which  will  hold  its 
voltage  substantially  constant  without  the  addition  of  more  or 
less  complicated  governing  mechanisms.  Such  a  system,  more- 
over, would  be  somewhat  unsafe  because  a  trifling  disarrange- 
ment of  the  electrical  connections  of  the  solenoid  might  cause  the 
governing  mechanism  to  increase  the  speed  without  limit  and 
thus  let  the  prime  mover  run  away.  On  account  of  these  and 
other  reasons  the  attempt  to  govern  the  current  or  voltage  of 
the  generator  by  changing  the  speed  has  been  practically  aban- 
doned. Engines,  water  wheels,  etc.,  intended  for  use  in  driving 
electric  generators  are  therefore  usually  provided  with  governors 
adapted  to  hold  the  speed  at  a  reasonably  constant  value. 

46.  Regulation  for  Constant  Potential. — The  Separately  Ex- 
cited Generator. — The  connections  of  a  machine  of  this  type  are 
shown  in  Fig.  30.     The  action  of  the  machine  as  regards  regula- 
tion is  best  shown  by  means  of  a  curve  connecting  the  terminal 
voltage  and  the  current  output  of  the  machine.     If  the  flux  were 
absolutely  constant  in  value  and  were  not  distorted  and  if  the 


46        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

speed  of  the  machine  did  not  vary,  the  internal  or  actual  gener- 
ated voltage  would  be  constant.  The  terminal  voltage  would  be 
less  than  this  on  account  of  the  drop  in  voltage  due  to  the 
passage  of  the  current  through  the  armature.  The  relation  be- 
tween these  quantities  is  shown  in  the  following  equation: 

E  =  Em-  RI, 

in  which  E  is  the  terminal  voltage  of  the  machine,  Em  is  the 
voltage  generated  in  the  armature,  /  is  the  current  in  the  armature, 
and  R  is  the  resistance  of  the  armature  and  brushes.  As  will 
appear  presently,  the  same  equation  applies  to  continuous  current 
motors  as  well  as  to  generators.  The  —  sign  before  RI  is  then 
changed  to  +  as  the  current  is  in  the  opposite  direction,  and  we 


FIG.  30. 

call  Em  the  back  e.m.f .  of  the  motor.     Em  is  always  less  than  the 
terminal  e.m.f.  in  a  motor  and  greater  in  a  generator. 

In  addition  to  the  RI  drop  in  the  armature,  we  must  consider 
the  effect  of  armature  reaction.  As  has  been  shown,  this  acts  to 
reduce  the  flux.  If  then,  the  speed  remains  constant,  the 
generated  voltage  will  decrease  slighty  as  the  current  is  increased. 
The  drop  due  to  armature  reaction  can  not  be  computed  exactly, 
since  it  depends  upon  the  shift  of  the  brushes  from  the  neutral 
position  as  well  as  upon  the  dimensions  of  the  machine.  We  have 
then,  the  following  two  factors  tending  to  cause  the  terminal 
voltage  to  fall  as  the  load  is  increased: 

A.  Drop  due  to  armature  resistance  =  RI. 

B.  Decrease  in  flux  due  to  armature  reaction. 

Figure  31  shows  the  curve  connecting  volts  and  amperes  in 
the  case  of  an  11-kw..  110- volt,  100-amp.  direct-current  generator. 


SYSTEMS  OF  DISTRIBUTION 


47 


The  field  was  separately  excited  and  the  field  current  and  the 
speed  were  constant.  It  will  be  seen  that  the  drop  in  voltage 
at  full  load  is  13  volts.  The  resistance  of  the  armature  of  this 
machine  is  0.04  ohms.  Since  the  full-load  current  is  100  amp., 
the  drop  in  the  armature  is  100  X  0.04  =  4.0  volts.  The  re- 
mainder of  the  drop,  9  volts,  therefore  is  due  to  armature 
reaction. 

As  previously  mentioned,  the  separately  excited  machine  is  not 
used  to  any  extent  in  direct- current  practice.  To  use  it  would 
require  an  exciter,  thus  adding  to  the  cost  and  complication. 


130 
120 

110 
100 


£70 

>  60 

50 

40 


\ 


0   10  20  30  40  50 


70  80  90  100  110  120  130  140  150  160  170  180  190  200 
Amperes 

FIG.  31. 


47.  The  Shunt-wound  Generator. — The  connections  of  a 
shunt  wound  machine  are  shown  in  Fig.  32.  In  a  machine  con- 
nected in  this  way,  the  two  causes  for  drop  in  voltage,  discussed 
in  connection  with  the  separately  excited  machine,  are  still 
operative.  However,  another  factor  is  introduced  which  causes 
the  voltage  to  drop  still  more.  In  the  separately  excited  machine 
the  field  current  is  constant,  since  it  is  not  influenced  in  any  way 
by  the  current  taken  from  the  machine.  In  the  shunt  machine, 
however,  the  field  current  is  equal  to  the  terminal  voltage  divided 
by  the  resistance  of  the  shunt  plus  that  of  the  connected  rheostat. 
This  resistance  is  constant,  but  since  the  terminal  voltage  drops 
somewhat,  due  to  the  two  causes  already  given,  the  current  taken 
by  the  shunt  will  also  decrease  as  the  load  is  increased.  The 


48        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

terminal  voltage  will  therefore  drop  off  more  in  the  shunt-wound 
machine  than  in  the  separately  excited  generator. 

For  light  loads,  the  drop  in  voltage  of  the  shunt- wound  machine 
is  about  double  that  of  the  separately  excited  generator  of  the 
same  capacity.  At  heavier  loads,  the  action  becomes  cumulative 
and  the  voltage  falls  very  rapidly.  Near  the  point  C  in  Fig.  33, 
any  increase  of  the  armature  current  causes  a  drop  in  terminal 
voltage,  and  this  in  turn  causes  a  decrease  in  the  field  current. 
This  again  reacts  to  make  the  voltage  drop  to  a  still  lower  value. 
At  this  load,  the  voltage  of  the  machine  has  become  unstable,  and 
any  attempted  increase  of  current  will  cause  the  machine  to  lose 
its  excitation  completely.  The  current  will  then  drop  nearly  to 
zero.  There  will  still  be  some  current  due  to  the  fact  that  there 


FIG.  32. 

is  some  residual  magnetism  in  the  field  magnets.  A  reduction 
of  the  external  resistance  to  zero  will  cause  the  current  to  drop 
to  the  value  shown  at  S  and  the  external  voltage  to  become  zero. 
It  is  clear  from  the  above  that  no  harm  would  result  if  a  shunt 
machine  were  short-circuited  and  then  put  in  motion.  The 
field  would  fail  to  build  up,  and  all  the  current  that  would  flow 
would  be  that  due  to  the  small  voltage  generated  by  the  residual 
magnetism.  It  should  not,  however,  be  inferred  that  a  machine 
in  operation  could  be  short-circuited  without  damage.  A  small 
machine  might  not  be  injured,  but  in  a  large  generator,  the  field 
magnetism  would  not  die  down  instantly  when  the  short  circuit 
was  established.  For  an  appreciable  time  the  machine  would  be 
operating  on  short  circuit  with  considerable  magnetism  in  the 
fields,  and  during  this  period  it  would  generate  an  excessive 


SYSTEMS  OF  DISTRIBUTION 


49 


current.  This  condition  would  last  only  for  a  few  seconds,  but 
during  this  time  considerable  damage  might  be  done. 

Figure  33  shows  the  characteristic  curve  of  the  same  generator 
that  was  used  in  getting  the  curve  of  Fig.  31,  but  the  machine 
was  shunt  wound  instead  of  being  separately  excited.  It 
appears  that  the  voltage  drops  much  more  for  a  given  current 
than  is  the  case  in  Fig.  31.  The  rapid  drop  in  voltage  when 
the  current  reaches  approximately  130  amp.  should  be  noted. 

For  good  operation  of  incandescent  lamps,  the  variations  in 
voltage  should  not  exceed  1  or  2  per  cent.  The  drop  in  voltage 
from  no  load  to  full  load  will  be  far  more  than  this  with  any  shunt 


J.3U 

120 
110 
1'JO 
90 
80 
70 

leo 

50 
40 
30 
20 
10 
0 

*••  ~. 

—  -^ 

-^^. 

--^ 

^•i.^. 

~~^ 

\ 

^ 

^ 

\ 

X 

x 

I 

"3 

\ 

£ 

\ 

c. 

i 

) 

~z 

^ 

^ 

^ 

^ 

a 

t 

.  " 

1 

^  — 

.—  -- 

^-^ 

[)  10  20  30  40  50  CO  70  80  90  100  110  120  130  140  150  160  170  180  190  20 
Amperes 

FIG.  33. 

generator  of  reasonable  size.  To  use  such  a  machine  in  constant- 
potential  service,  it  is  necessary  to  regulate  the  voltage  as  the  load 
changes  by  varying  the  resistance  of  the  field  rheostat.  Usually 
this  would  be  done  by  hand,  but  it  might  be  accomplished  by  some 
automatic  regulator.  The  compound- wound  generator,  however, 
is  generally  preferable  for  constant-potential  work,  as  it  can  be 
adjusted  to  maintain  its  voltage  constant  or  even  to  cause  the 
voltage  to  rise  as  the  load  increases. 

48.  The  Series-wound  Generator. — In  discussing  the  action 
of  the  series  machine,  it  is  necessary  to  consider  the  magnetiza- 
tion or  saturation  curve  of  a  generator.  Consider  a  shunt, 
series  or  compound-wound  machine,  connected  as  a  separately 


50        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


excited  dynamo  as  shown  in  Fig.  30.  The  field  current  is  varied 
from  zero  to  its  maximum  value.  No  load  is  connected  to  the 
machine  and  consequently  the  ammeter  in  the  armature  circuit 
reads  zero.  If  we  plot  the  field  currents  and  the  armature  volts, 
the  result  is  a  curve  like  the  upper  curve  of  Fig.  34.  With  zero 
current  in  the  field  circuit,  there  will  be  a  small  voltage  due  to 
the  residual  magnetism  in  the  field.  As  the  field  current  is  in- 
creased, the  voltage  will  also  rise.  The  voltage  will,  however,  not 
be  in  proportion  to  the  field  current.  It  will  be  strictly  propor- 
tional to  the  flux  passing  through  the  armature,  and  may,  in 
fact,  be  used  as  a  measure  of  this  flux.  The  flux  will  be  nearly 


130 
120 
110 
100 
90 


80 

570 
>60 
50 
40 
SO 
20 
10 


0  10  20  30  40  50  60  70  80  90  100  110  120  130  140  150  160  170  180  190  200 

Amperes 

FIG.  34. 

proportional  to  the  field  current  for  small  values  of  the  latter. 
For  larger  values  of  the  flux,  the  field  magnets  become  saturated, 
and  after  a  time  there  is  but  little  increase  of  the  flux  for  any  rea- 
sonable increase  of  the  field  current.  As  the  voltage  is  propor- 
tional to  the  flux,  it  will  increase  rapidly  at  first,  then  more 
slowly,  and  finally  will  increase  but  little.  It  is  clear,  however, 
that  it  will  never  decrease  for  an  increase  of  the  field  current. 

In  taking  the  volt-ampere  curve  of  a  series  machine,  the  connec- 
tions are  made  as  in  Fig.  22,  an  ammeter  being  connected  in  the 
circuit  and  a  voltmeter  across  the  terminals  of  the  machine. 
This  characteristic  will  be  similar  to  the  magnetization  curve  just 
discussed.  The  terminal  voltage  will,  however,  be  lower  than 


SYSTEMS  OF  DISTRIBUTION  51 

that  shown  on  the  magnetization  curve  for  any  given  current  on 
account  of  the  same  two  factors  previously  treated,  namely,  the 
armature  RI  drop  and  the  effect  of  armature  reaction.  In  ad- 
dition there  is  an  RI  drop  in  the  series  field.  The  curve  obtained 
is  shown  in  the  lower  curve  of  Fig.  34.  These  curves  were 
derived  from  the  same  small  generator  used  in  taking  the  curves 
of  Figs.  31  and  33,  only  the  series  winding  being  used.  It  will 
be  seen  that  for  large  currents  the  terminal  voltage  drops  as  the 
current  is  increased,  since  the  increased  effects  of  the  armature 
reaction  and  the  armature  and  series  field  RI  drop  are  greater 
than  the  slight  increase  of  generated  voltage  due  to  the  larger 
field  current.  In  the  machine  discussed  the  resistance  of  the 
armature  and  brushes  is  0.04  ohm.  That  of  the  series  field  is 
0.02  ohm,  or  0.06  ohm  in  all.  At  100  amp.  the  difference  of 
voltage  between  the  two  curves  is  9  volts.  The  drop  due  to 
field  and  armature  resistance  is  100  X  0.06  =  6  volts.  The  dif- 
ference, or  3  volts,  is  due  to  armature  reaction. 

It  will  be  apparent  at  once  that  a  characteristic  of  this 
sort  is  useless  in  a  machine  designed  for  constant  potential 
service.  However,  the  portion  of  the  curve  AB  approxi- 
mates a  constant  current.  This  will  be  particularly  the  case 
in  machines  with  large  armature  reaction.  Such  generators  were 
formerly  used  to  a  large  extent  for  constant  current  service, 
but  the  inherent  regulation  of  the  machines  was  hardly  good 
enough.  This  regulation  was  usually  supplemented  by  automatic 
regulators,  operating  to  shift  the  brushes,  shunt  some  of  the 
current  from  the  field  coils,  or  perform  some  similar  action  to  keep 
the  current  constant. 

49.  The  Compound-wound  Generator. — The  connections  of 
the  compound-wound  machine  are  shown  in  Fig.  23.  In  the 
case  of  generators,  the  series  coil  is  generally  wound  to  assist  the 
action  of  the  shunt  coil.  The  characteristic  of  the  machine  will 
be  a  compromise  between  that  of  the  shunt  machine  and  that  of 
the  series  machine.  By  properly  proportioning  the  number  of 
shunt  and  series  turns,  any  characteristic  between  that  of  Fig. 
33  and  that  of  Fig.  34  may  be  obtained.  Thus  in  Fig.  35  are 
shown  two  characteristics  of  the  machine  previously  referred  to. 
The  upper  one  was  taken  with  twenty-two  series  turns  on  the 
machine,  the  lower  with  sixteen.  In  the  case  of  the  lower  curve 
the  generator  is  said  to  be  flat  compounded,  since  the  voltage 
varies  but  little  from  zero  to  full  load.  In  the  upper,  where 


52        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

more  turns  are  used,  the  generator  is  overcompounded,  in  this 
case  about  10  per  cent. 

A  characteristic  of  the  type  given  by  a  compound  generator  is 
ideal  for  constant  potential  distribution,  and  since  it  can  be  ob- 
tained with  practically  no  extra  expense  or  complication,  com- 
pound-wound machines  are  in  practically  universal  use  for  this 
class  of  service.  The  generators  are  usually  overcompounded 
somewhat  to  allow  for  the  drop  in  speed  of  the  prime  mover,  and 
to  allow  for  the  loss  in  voltage  between  the  generator  and  the 
load.  By  using  a  proper  amount  of  compounding,  the  machine 
may  be  so  adjusted  that  the  voltage  at  the  load  remains  prac- 


130 
120 
110 
100 
90 


22  Series  Turns] 
-=f=j=- 

16  Series  i  urns 


SO 


70 


30 


20 


10 


0     10     20    80    40    50 


70     80    90    100   110   120  130   140  150  160   170  180  190  200 
Amperes 

FIG.  35. 


tically   constant   with  increase  in  load.     The   voltage   at    the 
generator  will  of  course  rise  somewhat. 

The  exact  action  of  the  series  coil  may  be  made  more  apparent 
by  a  numerical  example.  The  machine  from  which  the  fore- 
going curves  were  taken  has  4180  turns  in  the  shunt  field.  Oper- 
ating at  rated  speed  and  without  load,  it  was  found  that  the  shunt 
field  current  necessary  to  give  a  terminal  voltage  of  110  was  2.40 
amp.  Under  full  load,  it  was  necessary  to  increase  the  field  cur- 
rent to  2.80  amp.  to  maintain  the  voltage.  The  ampere  turns  at 
no  load  were 

4180  X  2.40  =  10,032 


SYSTEMS  OF  DISTRIBUTION  53 

and  at  full  load 

4180  X  2.80  =  11,704 

The  difference  was  1672  ampere  turns.  Since  the  full-load  cur- 
rent of  the  machine  was  100  amp.,  it  is  evident  that  sixteen  series 
turns,  carrying  the  entire  current  of  the  machine,  will  give 
16  X  100  =  1600  ampere  turns,  or  nearly  the  increase  in  the  shunt 
field  ampere  turns  required  in  order  to  maintain  the  voltage. 
It  is  apparent  from  the  curve  that  this  number  is  correct. 

Occasionally  a  generator  is  differentially  compounded,  that 
is,  the  series  turns  oppose  the  shunt  turns.  This  winding  is  used 
when  it  is  necessary  to  limit  the  output  of  a  generator  to  a  certain 
current,  as  when  a  dynamo  is  driven  from  a  windmill  operating 
without  a  governor,  and  is  used  to  charge  a  storage  battery;  or 
in  the  similar  case  of  a  lighting  generator  used  on  an  automobile 
to  keep  a  battery  charged  for  operating  the  lights  and  ignition. 
In  both  of  these  cases,  if  a  shunt-wound  generator  is  positively 
driven  so  that  its  speed  is  proportional  to  that  of  the  prime 
mover,  the  current  output  will  be  excessive  at  high  speeds. 
This  may  be  prevented  by  the  use  of  the  differentially  compounded 
machine,  since  the  series  winding  opposes  the  shunt,  and  if  the 
current  should  rise  to  a  high  enough  value,  would  completely 
neutralize  it.  This  current  is  then  the  limiting  current  of  the 
machine,  and  it  may  be  placed  at  any  desired  value  by  a  correct 
design  of  the  shunt  and  series  fields. 

50.  Method  of  Testing  Regulation. — The  regulation  of  a  direct- 
current  machine  may  be  shown  by  curves,  as  has  been  ex- 
plained. It  is  convenient,  however,  to  be  able  to  express  the 
regulation  by  a  simple  number.  Thus  if  we  say  that  a  certain 
shunt- wound  generator  regulates  within  5  per  cent.,  we  at  once 
have  a  basis  of  comparison  with  other  machines. 

To  obtain  the  regulation  of  a  shunt  or  separately  excited 
machine,  we  put  full  load  upon  the  dynamo  and  adjust  the  field 
until  the  voltage  is  the  rated  voltage  of  the  machine.  The  speed, 
of  course,  is  ajso  adjusted  to  the  rated  value.  The  main  switch 
is  then  opened  so  as  to  remove  all  of  the  load  from  the  machine. 
The  speed  will  doubtless  increase,  and  it  will  be  necessary  to  ad- 
just it  to  normal  again  or  else  make  a  correction  for  the  changed 
speed.  The  voltage  is  again  read.  The  rise  in  voltage  divided 
by  the  full-load  voltage  is  the  percentage  regulation.  Thus  if 
the  voltage  with  full  load  were  250  and  this  rose  to  275  when  the 


54        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

load  was  removed,  the  speed  remaining  constant,  the  regulation 
would  be 

275  _  250 

=  0.10  or  10  per  cent. 


Regulation  of  compound-wound  machines  is  not  of  great  im- 
portance and  is  rarely  required.  It  would  be  obtained  by  tak- 
ing the  characteristic  curve  as  shown  in  Fig.  35  and  obtaining 
the  maximum  deviation  of  the  curve  from  a  straight  line  connect- 
ing the  full-load  voltage  and  the  no-load  voltage.  This  deviation 
divided  by  the  full-load  voltage  is  the  regulation. 

The  percentage  of  overcompounding   is   defined  as  follows: 

..  full-load  e.m.f.  —  no-load  e.m.f. 

rer  cent,  overcompoundina;  =  - 

no-load  e.m.f. 

Thus  if  a  machine  gave  220  volts  at  no  load  and  250  volts  at  full 
load  at  the  same  speed,  we  should  have 

250  _  220 
Per  cent,  overcompounding  =  —  ^29  —  =  0-136  or  13'.6  per  cent. 

In  the  case  of  the  series  machine  the  term  regulation  as  used 
above  has  no  particular  value  and  is  not  employed. 

51.  Parallel  Operation  of  Generators.  —  In  early  days  of 
electrical  engineering  it  was  the  custom  to  operate  each  generator 
upon  a  circuit  of  its  own.  Each  power  house  had  a  number  of 
separate  circuits  all  ending  upon  a  common  switchboard.  When 
the  load  was  light  all  of  these  circuits  were  supplied  from  a  single 
generator.  When  the  load  increased  to  such  a  value  that  a  single 
machine  was  not  capable  of  carrying  it,  a  second  machine  was 
started  up  and  some  of  the  circuits  switched  to  it.  A  third 
generator  was  added  when  necessary,  and  so  on. 

With  this  method  of  operation  it  was  impossible  to  adjust  the 
load  on  the  different  machines  to  the  exact  value  desired.  More- 
over the  current  was  interrupted,  at  least  momentarily,  when  the 
load  was  transferred  from  one  machine  to  another,  causing  an 
objectionable  flicker  of  the  lights.  With  motors  on  the  circuit, 
there  was  considerable  chance  of  injury,  if  the  interruption 
was  for  more  than  a  fraction  of  a  second. 

This  method  of  operation  has  been  entirely  abandoned.  It 
is  now  the  custom  to  have  all  the  generators  feed  into  a  common 
system  of  mains,  known  as  bus-bars.  All  of  the  feeders  to  the 
different  circuits  are  connected  to  the  same  bus-bars.  Any 


SYSTEMS  OF  DISTRIBUTION  55 

number  of  machines  from  one  to  the  total  number  installed  may 
be  operated  at  one  time,  and  any  one  of  them  may  be  started  up 
or  shut  down  without  the  slightest  disturbance  of  the  system. 

This  applies  to  alternating-  as  well  as  to  direct- current  circuits. 
In  fact,  the  tendency  is  to  extend  the  idea,  particularly  in  the 
case  of  alternating-current  systems,  and  operate  a  number  of 
power  houses  in  parallel.  These  may  be  separated  by  consider- 
able distances  from  one  another.  This  method  tends  to  insure 
continuity  of  service,  since  the  crippling  of  a  single  power  house 
does  not  interfere  with  the  supply  of  power  from  the  other 
stations.  It  also  tends  to  economy  since  water  power  plants 
may  be  operated  in  parallel  with  steam  stations,  the  former  supply- 
ing the  power  when  the  flow  of  water  is  sufficient,  the  latter  being 
called  upon  to  supply  all  or  a  part  of  the  output  during  the  dry 
season.  It  may  also  happen  when  operating  a  number  of  water 
power  plants  in  parallel  that  the  water  for  the  different  plants 
comes  from  different  sources,  and  consequently  the  dry  seasons 
may  not  occur  at  the  same  time.  Thus  a  steam  reserve  may  be 
avoided. 

52.  Shunt  Generators  in  Parallel. — The  connections  of  two 
shunt  machines  with  the  necessary  instruments  are  shown  in  Fig. 
36.  Each  generator  has  a  shunt  field  rheostat,  a  double  pole,  single 
throw  switch  and  an  ammeter.  A  voltmeter  is  also  provided 
and  a  switch  to  connect  it  to  either  of  the  machines.  Assume 
that  the  machine  A  is  in  operation  and  that  the  load  is  such 
that  it  is  necessary  to  start  generator  B  also.  The  steam  en- 
gine, water  wheel  or  other  prime  mover  connected  to  B  is  set  in 
motion,  and  run  up  to  full  speed.  The  attendant  then  reads  the 
voltage  of  the  machine  A  or,  what  is  nearly  the  same  thing,  takes 
a  reading  of  the  voltage  directly  across  the  bus-bars.  He  then 
connects  his  voltmeter  to  the  machine  B  and,  by  means  of  the 
field  rheostat,  adjusts  the  voltage  of  B  until  it  is  the  same  as  that 
of  the  bus-bars.  The  switch  S'  is  then  closed,  thus  connecting  B 
to  the  load.  If  the  adjustment  of  the  voltage  is  exact,  no  current 
at  all  will  flow  when  the  switch  is  closed,  since  the  voltages  of  the 
line  and  that  of  machine  B  will  be  exactly  balanced.  To  make  5 
take  its  share  of  the  load,  it  is  merely  necessary  to  cut  out  some  of 
the  resistance  in  its  field  circuit.  This  raises  the  voltage  of  B 
and  causes  it  to  force  current  into  the  line.  Since  the  e.m.f. 
across  the  line  does  not  change  materially,  the  total  current 
flowing  to  the  load  does  not  change.  It  follows,  therefore,  that 


56        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

the  current  of  A  must  decrease  by  the  amount  of  current  B 
is  generating.  The  procedure  as  described  results  in  a  slight 
increase  in  voltage  across  the  line.  It  is  therefore  better  to  cut 
resistance  into  the  field  of  A  at  the  same  time  that  it  is  being  cut 
out  of  the  field  of  B.  In  this  manner  it  is  possible  to  transfer 
the  load  from  one  machine  to  another  with  no  disturbance  to  the 
voltage  or  interruption  of  service. 


FIG.  36. 

53.  Compound-wound  Generators  in  Parallel. — Although  the 
foregoing  arrangement  of  apparatus  gives  good  results,  shunt- 
wound  machines  are  rarely  used.  At  a  very  small  additional 
expense,  compound- wound  machines  can  be  bought.  These  will 
have  the  very  great  advantage  of  holding  their  voltage  very 
nearly  constant  with  changes  of  the  load,  or  of  increasing  their 
voltage  if  desired  with  increase  of  load.  Since  they  present 
practically  no  added  complication  or  greater  cost,  they  are  almost 
universally  preferred. 

However,  with  compound  machines  it  becomes  necessary,  at 
least  if  the  machines  are  at  all  overcompounded,  to  introduce  an 
added  connection,  called  an  equalizer,  between  the  machines. 
The  connection  in  simplified  form  is  shown  in  Fig.  37.  Suppose 
that  both  machines  are  overcompounded  and  that  the  equalizer 
is  not  present.  Let  the  load  on  the  two  be  the  same,  and  suppose 
that  for  some  reason  the  steam  engine  driving  one  of  the  machines 
speeds  up  a  trifle.  The  voltage  of  this  machine  will  be  increased, 
and  its  current  will  also  increase.  This  increase  of  current  will 
cause  the  voltage  to  rise  still  more,  since  all  the  current  passes 


SYSTEMS  OF  DISTRIBUTION 


57 


through  the  series  field.  This  action  will  continue  until  one 
machine  has  lost  all  its  load  and  has  in  fact  reversed  and  is  oper- 
ating as  a  motor,  while  the  other  machine  will  be  carrying  all 
the  load  and  driving  its  mate  as  well.  The  combination  would 
therefore  be  unstable  and  would  not  operate  long  in  this  way. 

All  this  is  remedied  by  the  simple  device  of  the  equalizer. 
This  is  made  of  heavy  copper  so  that  its  resistance  is  negligible 
compared  with  that  of  the  series  fields.  The  result  is  that  when 
the  current  comes  to  the  equalizer  it  divides  into  equal  parts,  if 
the  two  machines  are  identical,  even  though  the  currents  in  the 
two  armatures  are  not  the  same.  Since  the  two  shunt  fields  are 
the  same  while  the  two  series  fields  are  kept  the  same  by  the 
equalizer,  it  is  evident  that  the  voltages  of  the  two  machines 

200  Amp. 


150  Amp. 


50  Amp. 


V, 

^    r  -^ 

7~/ 

^^  Equalizer 

C^ 

V99 

0 

rv- 

o 

0 

O  wo  AmP- 

O  100  Amp. 

FIG.  37. 

must  be  nearly  the  same,  and  they  will  therefore  always  divide 
the  load  in  the  proper  proportion.  If  the  machines  are  of 
unequal  sizes,  the  larger  machine  will  have  the  lower  resistance 
in  its  series  field.  This  field  will  therefore  take  the  larger  current 
as  it  should. 

A  more  elaborate  connection  diagram  is  given  in  Fig.  38. 
Starting  from  the  bus-bars,  the  current  first  passes  through  a 
double-pole  circuit  breaker,  designed  to  protect  the  machine  from 
overload.  The  main  switch  has  three  poles  so  that  the  equalizer 
connection  is  closed  at  the  same  time  that  the  main  circuit  is 
closed.  The  operation  of  connecting  a  new  generator  to  the  line 
is  the  same  as  in  the  case  of  the  shunt  machine,  except  that  the 
voltage  should  preferably  be  slightly  below  that  of  the  bus-bars 
when  the  switch  is  closed.  As  soon  as  the  equalizer  connection 


58        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

is  closed,  some  current  will  flow  through  the  series  field  of  the 
incoming  machine,  and  will  raise  its  pressure  a  few  volts.  After 
a  little  experience,  the  attendant  can  readily  make  allowance  for 
this.  The  output  is  then  increased  by  cutting  resistance  out  of 
the  shunt  field  circuit  of  the  incoming  machine.  To  shut  down  a 
machine,  the  current  is  reduced  to  zero  or  at  least  to  a  small  value, 
the  main  switch  is  quickly  opened  and  the  circuit  breaker  is 
tripped. 

Any  number  of  such  machines  may  be  operated  in  parallel. 
Two  power  houses  may  also  be  connected  in  parallel.  If  they 
are  close  together,  it  may  be  necessary  to  install  an  equalizer 
between  them.  However,  they  are  usually  at  some  distance,  and 


mm 

FIG.  38. 


the  drop  in  potential  is  generally  great  enough  to  prevent  the 
voltage  from  rising  as  the  load  is  increased.  The  equalizer 
therefore  becomes  unnecessary. 

54.  Effect  of  Voltage  upon  the  Amount  of  Copper  Required. — 
The  higher  the  voltage  at  which  we  operate  a  circuit,  the  less 
the  weight  of  copper  required;  in  fact,  for  a  given  loss,  the 
amount  of  copper  required  varies  inversely  as  the  square  of  the 
voltage.  This  can  be  readily  shown  as  follows: 

E2 

Power  lost  =  P  =  PR  =  -, 

ti 

or  for  a  given  loss  the  resistance  varies  as  the  square  of  the  voltage. 
Since  the  weight  of  the  wire  varies  inversely  as  the  resistance, 


SYSTEMS  OF  DISTRIBUTION  59 

the  weight  varies  inversely  as  the  square  of  the  voltage.  Thus 
if  we  should  compute  the  weight  of  copper  required  to  transmit 
a  certain  amount  of  power  a  given  distance  at  a  pressure  of  220 
and  again  at  2200  volts,  we  should  find  that  for  the  same  loss  the 
former  case  would  require  100  times  as  much  copper  as  the  latter. 
The  importance  of  working  at  the  highest  possible  voltage  will  be 
apparent.  Long-distance  transmission  lines  are  now  operated 
at  pressures  as  high  as  150,000  volts. 

55.  The  Three-wire  System. — Most  incandescent  lamps  are 
constructed  for  a  potential  of  approximately  110  volts.  Lamps 
are  built  for  double  this  voltage,  but  for  the  same  candle 
power  the  filament  is  twice  as  long  and  of  half  the  cross  section. 
The  lamps  are  therefore  far  more  fragile  and  burn  out  quicker 
in  service.  They  are  also  more  expensive  to  make.  From  the 
standpoint  of  the  amount  of  copper  required  to  transmit  the 
power  to  them,  they  are  far  superior  to  the  110- volt  lamps,  but 

4-  Conductor 


Neutral 


10 


—  Conductor 

FIG.  39. 

they  are  so  far  inferior  in  other  respects  that  they  are  but  little 
used. 

By  using  the  three-wire  system  illustrated  in  Fig.  39  it  is 
possible  to  operate  at  a  voltage  of  220  and  yet  apply  a  voltage  of 
only  110  to  the  lamps.  If  the  lamps  on  the  two  sides  of  the 
system  take  exactly  the  same  current,  no  current  will  return  by 
way  of  the  neutral  wire.  By  care  in  the  grouping  of  the  lamps  on 
the  two  sides  this  condition  can  be  approximated  in  practice,  and 
the  drop  on  the  neutral  wire  becomes  negligible. 

If  the  neutral  wire  were  not  present^  this  system  would  require 
only  25  per  cent,  as"  much  copper  as  the  110- volt  system.  The 
neutral  is  usually  made  of  half  the  cross  section  of  the  outer  wires. 
The  total  amount  of  copper  is  then  25  per  cent.  +  6.25  per  cent. 
=  31.25  per  cent,  as  much  as  in  the  two- wire  system.  The  sav- 
ing of  copper  is  so  great  that  the  three-wire  system  is  universally 
used  whenever  a  large  amount  of  direct-current  power  must  be 
distributed  over  a  considerable  area. 


60       PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

Figure  39  shows  that  the  main  generator  operates  at  220  volts. 
The  two  small  dynamo  machines  are  mounted  on  a  common 
bedplate  with  their  shafts  coupled  together.  They  are  shown 
shunt  wound,  but  are  frequently  compound  wound.  If  the  sys- 
tem is  balanced,  both  machines  operate  as  motors  without  load. 
If  one  side  of  the  system  is  loaded  more  than  the  other,  its  vol- 
tage tends  to  drop.  As  soon  as  this  takes  place,  the  voltage  of  the 
line  on  that  side  becomes  less  than  the  back  e.m.f.  of  the  corre- 
sponding machine  and  the  latter  operates  as  a  generator.  Mean- 
while the  voltage  on  the  other  side  has  risen  and  the  other 
machine  develops  more  power  as  a  motor  and  drives  the  machine 
which  is  operating  as  a  generator.  In  this  way,  the  load  on  the 
two  sides  is  equalized  and  the  voltages  are  kept  near  their  proper 
values. 

PROBLEMS 

19.  Four  incandescent  lamps  are  connected  to  110-volt  mains  in  the  same 
manner  as  those  of  Fig.  29.     Their  resistances  are  respectively  100,  110,  120 
and  130  ohms.     What  is  the  current  in  each  lamp?     The  total   current? 
What  is  the  resistance  of  all  the  lamps  in  parallel,  i.e.,  what  single  resistance 
would  take  the  same  current  from  the  line  as  the  four  resistances  in  parallel  ? 

20.  If  the  above  lamps  are  1  mile  from  the  generating  station  and  are  fed 
through  a  pair  of  No.  10  B  and  S  wires,  what  is  the  voltage  at  the  generating 
station  if  the  voltage  at  the  lamps  is  110?     The  resistance  of  No.  10  wire  is 
1  ohm  per  1000  ft. 

21.  The  potential  at  the  terminals  of  a  shunt- wound  d.-c.  generator  is  250 
volts,  and  the  current  is  1000  amp.     If  the  resistance  of  the  armature  is 
0.0035  ohm,  what  is  the  generated  voltage? 

22.  A  compound-wound  dynamo  generates  230  volts  when  operating  at 
no  load  and  at  normal  speed.     At  full  load  with  the  same  shunt  field  current 
and  an  output  of  300  amp.  it  generates  250  volts  at  the  terminals.     What  is 
the  internal  voltage  if  the  resistance  of  the  armature  is  0.012  ohm?     What 
is  the  percentage  increase  in  the  flux  passing  through  the  armature  due  to 
the  series  field? 

23.  A  certain  d.-c.  generator  gave  its  rated  e.m.f.  (110  volts)  at  rated  speed 
with  a  shunt  field  current  of  2.5  amp.     With  full  load  of  100  amp.  applied 
it  was  necessary  to  increase  the  shunt  field  current  to  2.90  amp.  to  hold  the 
voltage  constant,  the  speed  being  the  same.     If  there  are  1600  turns  of  wire 
in  each  shunt  field  coil,  how  many  series  turns  per  coil  will  it  be  neces- 
sary to  add  in  order  that  the  machine  may  be  flat  compounded?     The  drop 
due  to  the  series  coil  may  be  neglected. 


CHAPTER  V 
CHARACTERISTICS  OF  MOTORS 

56.  Characteristics  of  Motors. — In  the  case  of  continuous- 
current  generators,  the  speed  is  constant  or  approximately  so, 
and  the  variables  are  the  terminal  voltage  and  the  current.     In 
plotting  characteristic  curves,  the  voltage  and  current  are  there- 
fore usually  the  quantities  chosen.     In  the  case  of  motors,  since 
practically  all  are  operated  on  the  constant  potential  system,  the 
terminal  voltage  may  be  considered  as  constant.     The  principal 
variables  are  then  the  speed,  current,  torque,  kilowatts  input 
and  output  in  kilowatts  or  in  horse  power.     The  ratio  of  the  out- 
put to  the  input  or  the  efficiency  is  also  frequently  required.     In 
performance  curves  of  motors,  currents  are  usually  plotted  as 
abscissae,  and  the  other  values  as  ordinates. 

Of  the  above  values,  the  speed  and  the  torque  are  perhaps  the 
simplest  to  study  in  gaining  an  elementary  notion  of  the  operation 
of  a  motor.  They  are  also  of  value  in  comparing  the  electric 
motor  with  other  sources  of  power. 

57.  Operation  of  same  Machine  either  as  a  Generator  or  as 
a  Motor. — As  previously  explained,  the  action  of  a  dynamo  is 
essentially  the  same  whether  it  is  operating  as  a  generator  or  as  a 
motor.     Assume  that  a  shunt  machine  is  driven  by  some  outside 
power  at  the  proper  speed  and  that  by  means  of  the  field  rheostat 
its  voltage  is  adjusted  so  as  to  be  the  same  as,  and  in  the  opposite 
direction  to,  that  of  a  pair  of  constant  potential  mains.    A  volt- 
meter should  be  used  which  will  reverse  its  deflection  if  the  vol- 
tage is  reversed.     By  connecting  first  to  the  mains  and  then  to  the 
machine,  the  operator  can  assure  himself  that  the  two  voltages 
are  equal  and  opposite.     (See  Fig.  36.)     If  the  switch  connecting 
the  machine  to  the  line  be  closed,  no  current  will  flow.     The  e.m.f. 
of  the  line  will  be  just  balanced  against  that  of  the  machine  and 
the  resultant  voltage  acting  around  the  circuit  will  therefore  be 
zero.     The  machine  is  acting  neither  as  a  generator  nor  as  a 
motor. 

If,  now,  the  speed  of  the  prime  mover  be  slightly  increased,  the 

61 


62        PRINCIPLES  0?  DYNAMO  ELECTRIC  MACHINERY 

e.m.f.  of  the  machine  will  become  greater  than  that  of  the  line 
and  consequently  there  will  be  an  unbalanced  voltage.  A  current 
equal  to  the  difference  of  the  two  voltages  divided  by  the  re- 
sistance of  the  armature  of  the  machine  will  flow.  This  current 
will  be  in  the  same  direction  as  the  e.m.f.  of  the  dynamo,  and  the 
machine  will  therefore  act  as  a  generator  and  deliver  power  to 
the  line.  As  explained  in  Art.  32,  since  the  current  and  the  e.m.f. 
of  the  machine  are  in  the  same  direction,  the  torque  due  to  the 
current  will  be  in  such  a  direction  as  to  oppose  the  motion.  The 
prime  mover  must  therefore  develop  more  power  in  order  to 
maintain  the  rotation. 

If,  on  the  other  hand,  instead  of  increasing  the  speed,  we  de- 
crease it,  the  reverse  action  will  take  place.  The  voltage  of  the 
machine  will  become  less  than  that  of  the  line.  The  difference 
of  the  two  voltages  will  act  as  before  to  force  current  through 
the  armature  of  the  machine,  but  since  the  line  e.m.f.  will  now 
be  the  stronger,  the  flow  of  current  will  be  in  the  reverse  direc- 
tion. The  torque  will  also  be  reversed  or  the  machine  will  act 
as  a  motor. 

If  now  the  load,  i.e.,  the  torque  on  the  motor  shaft,  be  increased, 
the  machine  will  slow  down.  This  immediately  results  in  a  still 
further  reduction  of  the  back  e.m.f.  of  the  motor  and  a  greater 
difference  between  the  line  voltage  and  that  of  the  machine. 
More  current  will  now  flow  through  the  armature  of  the  machine 
and  the  latter  will  develop  more  torque.  The  slowing  down  of 
the  machine  will  continue  until  the  increased  torque,  due  to  the 
larger  current  is  sufficient  to  overcome  the  resistance  of  the 
load.  The  motor  will  then  continue  to  operate  at  this  speed. 

The  slowing  down  of  the  motor  in  order  to  allow  the  necessary 
current  to  pass  need  not  be  large.  Thus  in  the  case  of  the 
machine  used  as  a  generator  in  obtaining  the  curves  of  Figs.  31, 
33,  34,  and  35,  since  the  resistance  of  the  armature  is  0.04  ohms, 
a  voltage  of  only  100  X  0.04  =  4  volts  is  required  to  force 
full-load  current  through  the  armature.  Since  the  terminal 
potential  is  110  volts,  this  requires  a  reduction  in  back  e.m.f. 
and  a  corresponding  reduction  in  speed  of  only  4  -f-  110  =  3.64 
per  cent. 

Instead  of  changing  the  speed  as  explained  above  to  cause  the 
machine  to  act  either  as  a  generator  or  as  a  motor,  the  same 
result  can  be  secured  in  another  way.  If,  when  the  machine 
is  operating  at  such  a  speed  that  the  voltage  generated  by 


CHARACTERISTICS  OF  MOTORS  63 

the  machine  is  the  same  as  that  of  the  line  (and  in  consequence 
the  current  is  zero)  the  field  is  strengthened  by  cutting  out 
some  of  the  resistance  in  the  field  circuit,  the  voltage  of  the 
machine  will  exceed  that  of  the  line.  The  machine  will  then  force 
current  in  the  direction  of  its  own  e.m.f  .  or  it  will  become  a  gener- 
ator. A  further  increase  in  the  field  strength  will  furnish  still 
more  current.  In  this  manner  the  load  on  each  of  a  number  of 
machines  operating  on  the  same  circuit  is  adjusted  to  make  each 
take  its  proper  share  of  the  load. 

If,»on  the  other  hand,  the  field  is  weakened,  the  e.m.f.  of  the 
line  will  be  greater  than  that  of  the  machine,  current  will  flow 
against  the  back  e.m.f.  or  the  machine  will  operate  as  a  motor. 
A  further  weakening  of  the  field  will  cause  the  machine  to  take 
more  current  and  consequently  develop  more  power  and  torque 
as  a  motor.  If  the  resisting  torque  of  the  load  remains  the  same, 
the  motor  will  develop  more  torque  than  is  required  by  the  load, 
and  the  motor  will  speed  up.  This  in  turn  will  increase  the  back 
e.m.f.  until  it  is  more  nearly  equal  to  the  line  e.m.f.  The  current 
will  then  decrease  until  just  sufficient  torque  is  developed  to  keep 
the  load  in  motion.  It  is  important  to  note  that  a  weakening  of 
the  field  results  in  an  increase  of  speed.  This  is  contrary  to  what 
one  might  expect  at  first  thought. 

58.  The  Fundamental  Equation  of  the  Direct-current  Motor.  — 
The  foregoing  principles  can  be  better  brought  out  by  a  con- 
sideration of  the  fundamental  equation  of  the  motor.  This 
was  developed  in  Art.  46;  in  connection  with  the  study  of  the 
machine  as  a  generator.  As  explained,  the  action  as  a  generator 
or  as  a  motor,  is  essentially  the  same.  The  difference  is  merely  a 
question  of  whether  the  voltage  of  the  machine  is  higher  or  lower 
than  that  of  the  line  to  which  it  is  connected.  The  sign  of  the 
current  is  changed  since  it  is  in  the  opposite  direction  in  a  motor 
to  that  in  a  generator  and  we  may  then  write 

E  =  Em  +  RI 

As  we  have  previously  shown  the  back  e.m.f.  developed  by  the 
motor  is  (see  Art.  36) 

Em  =  3>nN  +  108 


Omitting  the  constant  108  for  the  sake  of  simplicity  we  may  re- 
write the  equation  in  the  following  form: 

E  =  3>inN  +  RI 


64        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

and  solving  for  n  we  obtain  the  expression 

E^-_  #7 

In  which  n  =  the  revolutions  per  second,  E  is  the  line  voltage, 
R  is  the  resistance  of  the  armature,  /  is  the  current  in  the  arma- 
ture, $1  is  the  magnetic  flux  per  pole  (measured  in  units  of  108 
lines),  and  N  is  the  number  of  conductors  connected  in  series 
between  brushes,  times  the  number  of  poles. 

In  considering  the  formula,  it  must  be  remembered  that  the 
quantity  RI  in  motors  of  reasonable  size,  is  always  very  small 
compared  to  the  value  of  E.  In  a  small  motor  at  full  load,  it 
may  be  as  much  as  10  per  cent.  In  a  motor  of  say  1000  hp.  it 
would  probably  not  be  greater  than  1  per  cent.  This  means  that 
the  speed  n  will  not  vary  more  than  this  percentage  when  the  load 
and  consequently  7,  is  varied  from  zero  to  full-load  value,  pro- 
viding $  remains  constant.  This  is  nearly  the  case  in  a  shunt- 
wound  motor.  To  be  more  exact,  in  the  shunt  machine  the 
brushes  usually  have  a  slight  forward  lead  and  in  consequence  of 
the  armature  reaction  $  will  usually  decrease  somewhat  as  the 
armature  current  increases.  (See  Art.  42.) 

59.  Speed  Torque  Curve  of  Shunt  Motor. — The  speed  torque 
curve  of  an  actual  shunt  motor  is  plotted  in  Fig.  40.  The  torque 
is  proportional  to  the  number  of  conductors  on  the  armature, 
the  current  and  the  flux.  The  number  of  conductors  N  is 
constant.  The  current  7  is  a  variable.  The  flux  <f>  is  nearly 
constant  but  decreases  somewhat  as  the  current  increases.  On 
this  account  the  curve  of  speed  and  torque  is  not  a  straight 
line. 

The  point  of  full-load  torque  is  shown  on  the  curve,  and  it 
will  be  seen  that  the  torque  at  this  point  is  only  a  small  fraction 
of  the  maximum  torque  that  the  motor  can  develop.  The 
maximum  overload  torque  is  also  indicated.  It  is  important  to 
note  that  the  motor  is  not  worked  at  anywhere  near  its  maximum 
torque.  If  an  attempt  were  made  to  do  so,  it  would  heat  up  very 
rapidly  and  burn  out  quickly.  Moreover  if  allowed  to  rotate  and 
develop  anywhere  near  its  full  torque,  there  would  be  prohibitive 
sparking  at  the  commutator,  and  the  efficiency  would  be  very 
low. 

These  remarks  apply  particularly  to  large  motors.  With  a 
motor  of  a  fraction  of  a  horse  power  it  is  frequently  possible  to 


CHARACTERISTICS  OF  MOTORS 


65 


apply  the  full  potential  of  the  line  to  start  the  motor,  so  that  we 
are  operating  for  an  instant  at  the  point  S.  This  method  of 
operation  would  not  do  for  large  motors,  and  in  this  case  we  must 
use  a  starting  rheostat.  (See  Chap.  VI.)  It  is  clear  that  the  motor 
has  the  ability  to  develop  enormous  starting  torque  and  there  is 
therefore  never  any  difficulty  with  a  shunt-  or  series-wound 
direct-current  motor  in  developing  all  the  torque  that  is  neces- 
sary to  start  any  load  within  the  capacity  of  the  motor.  This  is 
by  no  means  the  case  with  alternating-current  motors  as  will 
appear  later. 


r.p.m 
2000 

1800 
1600 
1400 
1200 
1000 
£800 

a 

600 
400 
200 

0 
1 

I 



-»^L 

—  — 

-•K, 

>* 

"-•X, 

)verload 

^ 

\ 

!•- 

?>- 

&H 

"X 

X 

a 

N 

? 

3 

\ 

3 

\ 

s 

)  40  80  120  1GO  200  240  280  320  360  400  440  480  520  5GO  600ft.lbs. 
Torque 

FIG.  40. 

60.  The  Series-wound  Motor. — The  analysis  of  the  action  of 
the  series- wound  motor  is  made  somewhat  more  difficult  by  the 
fact  that  the  ftux  <£  is  not  constant.  The  whole  current  taken 
by  the  motor  passes  through  the  series  field,  and  consequently  an 
increase  in  current  results  in  an  increase  in  the  field  strength. 
We  cannot  embody  the  facts  in  a  mathematical  equation  because 
the  field  strength  bears  no  simple  relation  to  the  strength  of 
the  current  through  the  field  winding.  This  is  on  account  of  the 
magnetic  saturation.  It  might  appear  that  we  could  derive  an 
empirical  equation.  This  could  be  done  in  the  case  of  any 
particular  motor,  but  the  expression  would  not  be  applicable  to 
any  other  machine  since  the  quality  of  the  iron,  degree  of  satura- 
tion, etc.,  would  be  different.  It  is  enough  for  the  present  to 
know  that  <£  increases  with  an  increase  in  the  value  of  the  cur- 

5 


66        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


rent,  but  that  the  rate  of  increase  becomes  very  small  with  large 
values  of  the  current. 

Considering  again  the  equation  of  the  motor,  an  increase  of  the 
torque  of  the  load  connected  to  a  series  motor  results,  as  in  the 
shunt  motor,  in  a  decrease  of  speed.  The  back  e.m.f.  at  once 
becomes  less  and  since  the  difference  between  the  back  e.m.f.  and 
the  line  voltage  is  increased,  the  current  increases.  This,  in  turn, 
results  in  an  increase  in  the  flux.  This  latter  action  was  absent 
in  the  case  of  the  shunt  machine.  The  increase  of  flux  results  in 
a  higher  back  e.m.f.  than  would  otherwise  be  present,  and 
consequently  part  of  the  effect  of  the  decrease  in  speed  is  neutral- 
ized. It  follows  that  to  obtain  a  given  increase  in  current,  the 
series  motor  must  slow  down  far  more  than  the  shunt  machine. 


r.p.m. 
2000 


1800 

1600 

1400 

1200 

,1000 

\  800 

600 

400 

200 


\ 


2!-*! 


i 


0  40   80  120  100  200  240  280  320  360  400  440  480  520  560  600ft.lbs. 
Torque 

FIG.  41. 

In  the  shunt  machine,  the  torque  is  nearly  proportional  to  the 
current  in  the  armature,  since  the  flux  is  practically  constant. 
In  general  the  torque  is  proportional  to  the  product  of  the  flux, 
the  armature  current  and  the  number  of  conductors  on  the  arma- 
ture. In  the  series  motor  the  flux  increases  as  the  current  in- 
creases. If  the  increase  of  flux  were  proportional  to  the  increase 
of  current,  the  torque  would  be  proportional  to  the  square  of  the 
current.  This  is  nearly  the  case  for  small  values  of  the  current. 
For  larger  currents,  however,  the  increase  of  the  flux  is  far  less 
than  the  increase  of  the  current,  and  the  torque  therefore  in- 
creases faster  than  the  current  but  not  in  proportion  to  the  square 
of  the  current.  The  net  result  of  these  actions  is  a  speed  torque 


CHARACTERISTICS  OF  MOTORS 


67 


curve  of  the  shape  indicated  in  Fig.  41.  This  curve  shows  that 
the  line  will  never  cross  the  axis  of  zero  torque,  no  matter  what 
the  speed  is.  An  increase  in  speed  results  in  a  decrease  of  current 
and  a  consequent  weakening  of  the  field  strength.  Therefore  no 
matter  how  fast  the  machine  may  be  driven,  its  back  e.m.f.  will 
never  exceed  that  of  the  line,  and  consequently  it  can  not  reverse 
and  become  a  generator.  Also  if  the  torque  required  to  maintain 
the  load  in  motion  is  very  small  or  is  entirely  removed,  the  motor 
will  speed  up  to  an  excessive  speed.  It  might  readily  reach  such 
a  speed  that  the  conductors  would  be  thrown  out  of  the  slots  by 
centrifugal  force  and  the  motor  seriously  damaged.  Series  motors 
are  therefore  used  only  on  loads  which  can  not  be  reduced  to  a 
small  value  or  they  are  applied  to  classes  of  service  where  an 
attendant  is  always  present  to  control  the  speed. 

61.  The  Compound-wound  Motor. — The  series  coil  on  a  com- 
pound-wound motor  may  be  wound  to  assist  the   shunt   or  to 


zuuu 
1800 

IfiOO 

1400 

1200 

^v 

1000 

^ 

L^ 

§J  OQO 

T3 

i 

•o 

K5 
O 

^ 

\ 

i^ouu 
CO 
(500 

3 

'SI- 

t+ 
O 
| 

^"""-•v 

\ 

400 

c£ 

*% 

a 

^^s 

\ 

200 

"a 
sl 

s> 

V^ 

0 

3 

X, 

\ 

0  40   80  120  160  200  240  280  320  360  400  440  480  520  560  GOOft.lbs. 
Torque 

FlG.  42. 

oppose  it.  The  latter  connection  is  rarely  used,  while  the  former 
is  in  common  use.  The  two  connections  are  known,  respectively, 
as  cumulative  compounding  and  differential  compounding. 

A  cumulative  compound  motor  is  intermediate  in  its  character- 
istics between  the  series-  and  the  shunt- wound  motor.  There  is 
always  present  a  certain  amount  of  flux  in  the  field,  due  to  the 
shunt  winding  and  this  is  independent  of  the  current  in  the 
armature.  In  addition,  as  the  armature  current  increases,  the 
flux  is  increased  by  the  action  of  the  series  coil.  The  character- 


68        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

istics  of  the  motor  will,  therefore,  be  nearly  the  same  as  those  of 
the  shunt  motor  if  the  number  of  series  turns  is  small,  or  on  the 
other  hand,  they  will  approach  those  of  the  series  machine  if  the 
number  of  series  turns  is  large.  It  is  standard  practice  with  stock 
motors  to  supply  approximately  15  per  cent,  as  many  series 
ampere  turns  as  shunt  ampere  turns.  With  this  proportion  a 
motor  will  have  a  speed  torque  characteristic  approximating 
that  shown  in  Fig.  42.  The  motor  has  a  limiting  speed  like 
the  shunt  machine,  and  if  driven  above  this  speed  it  will  act  as  a 
generator.  It,  however,  slows  down  more  under  load  than  the 
shunt  machine.  This  is  advantageous  in  certain  applications  as 
will  be  shown  presently. 

62.  The  Differential    Compound    Motor. — Compound-wound 
motors  have  been  constructed  in  which  the  windings   were  so 


2000 
1800 


1600 


0   40  80  120  160  200  240  280  320  360  400  440  480  520  560  600ft.lbs. 

Torque 
FIG.  43. 

connected  that  the  series  field  opposed  the  shunt  field.  An 
increase  of  load  and  consequently  of  current  in  such  a  motor 
results  in  a  weakening  of  the  field.  This  weakening  of  the  field 
flux  may  be  sufficient  to  cause  the  motor  to  increase  somewhat  in 
speed  as  the  load  increases. 

The  speed  regulation  of  the  ordinary  shunt  motor  is  sufficiently 
good  so  that  there  is  little  demand  for  a  motor  with  still  better 
speed  regulation  or  even  an  increase  in  speed  with  an  increase 
in  load.  Moreover  there  are  several  rather  serious  objections  to 
such  a  motor.  Perhaps  the  most  obvious  is  that  if  an  attempt  is 
made  to  start  with  a  large  load  and  consequently  a  large  current, 


CHARACTERISTICS  OF  MOTORS  69 

the  action  of  the  series  coil  will  be  so  powerful  that  the  flux  will 
be  very  much  reduced  and  an  excessive  current  will  be  required. 
If  a  still  larger  current  is  passed  the  torque  will  be  reversed  and 
the  motor  will  tend  to  rotate  in  the  opposite  direction.  Such 
motors  are  rarely  used.  The  speed  torque  curve  of  this  motor  is 
shown  in  Fig.  43. 

In  Fig.  43  are  plotted  on  a  single  sheet  the  same  curves  as  are 
plotted  in  Figs.  40,  41,  and  42  to  aid  comparison  of  the  charac- 
teristics of  the  different  machines.  The  curves  are  those  of  a 
motor  rated  at  15  hp.  at  1200  r.p.m.  The  same  armature  and 
field  structure  are  used  in  all  three  cases  and  the  only  difference 
is  the  type  of  winding  on  the  field. 

63.  The  Choice  of  Motors  for  any  Particular  Service. — The 
Shunt  Motor. — For  work  which  requires  a  practically  constant 
speed,  irrespective  of  the  load,  the  shunt  motor  is  well  adapted. 
Examples  of  such  work  are  the  driving  of  line  shafts  to  which  a 
number   of   machines   are   belted,    the   operation   of   individual 
machine   tools,    such   as   lathes,    drill   presses,    planers,    milling 
machines,  woodworking  tools,  etc.     In  all  of  these  the  starting 
duty  is  moderate,  and  heavy  overloads  are  not  common. 

64.  The  Series  Motor. — As  the  torque  of  the  series  motor  is 
approximately  proportional  to  the  square  of  the  current,  it  fol- 
lows that   for   starting   heavy  loads  requiring  more   than   full- 
load  current,  it  is  superior  to  the  shunt  motor,  since  the  same  tor- 
que will  be  developed  with  less   current.     For  loads  less  than 
normal,  the  series  motor  is  correspondingly  inferior  in  starting 
to  the  shunt  motor.     Thus,  suppose  a  motor  were  required  to 
exert  merely  full-load  torque  during  starting.     Either  type  of 
motor  would  require  full-load  current,  and  both  would  be  equally 
effective.     However,  if  it  were  necessary  to  exert  four  times  full- 
load  torque,  the  shunt  motor  would  require  four  times  full-load 
current.     The  series  motor,  on  the  other  hand,  if  the  fields  were 
unsaturated,  would  require  only  twice  full-load  current.     This 
current  would  produce  a  field  of  double  strength,  and  this  in  com- 
bination with  the  double  armature  current  would  give  four  times 
the  normal  torque.     As  a  matter  of  fact,  the  field  would  be  satu- 
rated to  a  considerable  extent  in  a  commercial  motor,  and  the 
motor  would  require  more  nearly  three  times  full-load  current, 
instead  of  only  twice  this  quantity.     Even  with  this  qualification, 
the  superiority  of  the  series  motor  will  be  apparent. 

If,  on  the  contrary,  the  motor  were  required  to  develop  only 


70        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

one-half  of  normal  torque,  the  shunt  motor  would  require  one- 
half  of  normal  current.  The  series  motor  would  need  -\/0.5  = 
0.707  of  full-load  current. 

The  series  motor  also  differs  from  the  shunt  motor  in  that  it  is 
to  a  certain  degree  a  constant-power  machine;  that  is,  as  the 
torque  increases  on  a  series  motor,  it  slows  down  very  much. 
This  means  that  less  power  is  required  to  keep  the  load  in  motion 
than  would  be  the  case  if  nearly  full  speed  were  to  be  maintained. 
Hence  a  given  series  motor  will  be  able  to  handle  torques  that 
would  be  too  great  for  a  shunt- wound  motor.  This  feature, 
also  results  in  a  lessened  demand  upon  the  source  of  power. 
This  may  be  a  point  of  considerable  importance. 

As  an  example,  consider  the  application  of  electric  motors  to 
the  propulsion  of  cars.  Series  motors  are  always  used  in  this 
service.  As  compared  with  shunt  motors,  they  consume  less 
power  in  starting  and  accelerating  the  car.  This  is  very  im- 
portant, as  practically  the  whole  duty  of  the  motor  in  the  case  of 
city  cars  is  to  give  this  acceleration  to  the  car,  which  is  then  al- 
lowed to  coast  for  some  distance,  and  finally  is  stopped  by  the 
application  of  the  brakes. 

In  case  a  hill  is  to  be  climbed  or  heavy  snow  is  met,  the  series 
motor  will  slow  down,  and  continue  to  propel  the  car  with  less 
current  consumption  than  the  shunt  motor,  but  at  a  reduced 
speed.  Thus  it  continues  the  service,  whereas  the  shunt  motor 
would  be  so  overloaded  that  it  would  be  in  danger  of  burning  out. 

It  has  been  mentioned  that  the  shunt  motor,  if  driven  above 
normal  speed  will  act  as  a  generator  and  return  power  to  the  line. 
It  would  seem  that  this  property  might  be  exploited  to  return 
power  while  the  car  was  descending  hills.  This  can  be  done,  but 
the  number  of  hills  in  the  usual  urban  or  interurban  line  is  too 
small  to  make  the  possible  saving  from  this  source  important. 
However,  in  the  case  of  a  long  uniform  grade  up  a  mountain  side 
the  possible  return  of  power  while  the  cars  were  descending  might 
be  important  enough  to  justify  the  use  of  shunt  motors. 

Hoisting  service  as  applied  to  cranes  is  very  similar  in  many 
respects  to  car  service.  Series  motors  are  exclusively  employed 
for  this  class  of  work  also.  The  fact  that  a  light  load  is  auto- 
matically hoisted  rapidly,  and  a  heavy  one  more  slowly  is  of 
great  practical  importance. 

65.  The  Compound-wound  Motor. — A  typical  example  of  the 
class  of  service  to  which  the  compound-wound  motor  is  adapted 


CHARACTERISTICS  OF  MOTORS  71 

is  the  operation  of  a  punch  press.  The  average  power  require- 
ment of  a  punch  press  is  rather  low,  being  in  many  cases  not  much 
more  than  that  wasted  in  friction.  Just  at  the  moment  of  punch- 
ing, however,  the  power  rises  momentarily  to  a  high  value.  A  load 
of  this  character  is  best  handled  by  installing  a  flywheel  of  con- 
siderable size  on  the  motor  shaft.  While  the  punch  is  passing 
through  the  metal  sheet,  the  flywheel  slows  down  and  delivers 
the  energy  required  to  punch  the  hole.  If  a  shunt  motor  were 
used,  it  would  take  a  large  current  from  the  line  on  account  of  the 
slowing  down,  and  would  be  accelerated  at  a  correspondingly 
high  rate  to  the  original  speed.  This  would  result  in  drawing  a 
large  momentary  current  from  the  line  and  would  necessitate  a 
correspondingly  large  motor  to  commutate  the  current.  The 
compound- wound  motor  on  the  other  hand  does  not  take  so  large 
a  current  for  a  given  drop  in  speed.  A  smaller  motor  can  there- 
fore be  used,  and  the  power  demand  is  more  uniform.  A  series 
motor  is  not  suitable  since,  if  allowed  to  run  idle  for  some  time 
it  would  attain  a  dangerous  speed. 

Compound  motors  are  often  preferred  to  shunt  machines  in 
cases  where  close  speed  regulation  is  not  necessary  and  the  load 
is  of  such  a  nature  that  a  large  starting  torque  is  required. 
Compressors  for  refrigerating  plants  often  fall  in  this  category. 

66.  Direction  of  Rotation  of  Motors  and  Generators. — The 
direction  of  rotation  of  a  shunt  motor  may  be  reversed  by  revers- 
ing the  connections  of  either  its  armature  or  its  field.  The  direc- 
tion of  rotation  is  not  reversed  by  reversing  the  applied  voltage. 
The  field  is  reversed,  which  alone  would  cause  a  reversal  of  rota- 
tion, but  since  the  current  in  the  armature  is  also  reversed,  the 
result  is  that  the  direction  of  rotation  remains  the  same.  The 
same  remarks  apply  to  the  series  motor.  In  fact,  as  we  shall  see, 
a  series  motor  with  certain  alterations  to  prevent  excessive 
losses  and  heating,  may  be  operated  on  alternating  current. 

The  procedure  in  the  case  of  a  compound-wound  motor  is 
slightly  different.  To  reverse  the  direction  of  rotation,  we  should 
reverse  the  connections  of  the  armature  only,  or  else  those  of 
both  the  shunt  and  series  fields;  that  is,  we  should  not  treat  the 
armature  and  series  field  as  a  unit,  since  if  we  did  so  the  action 
of  the  series  field  on  reverse  would  be  the  opposite  of  that  desired. 

The  actions  of  the  corresponding  machines  as  generators  can 
be  readily  deduced  from  their  actions  as  motors.  Thus,  a  shunt 
machine  may  generate  with  a  certain  polarity  of  the  brushes. 


72        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

This  polarity  may  be  reversed  without  change  in  the  connections 
or  reversal  of  direction.  If  we  take  a  given  machine  which  has 
been  generating  with  a  certain  polarity,  and  pass  a  current 
through  the  shunt  field  in  the  reverse  direction  from  an  outside 
source  of  power,  we  shall  probably  reverse  the  residual  magnetism 
of  the  field.  When  the  machine  is  started,  the  polarity  will  be 
reversed,  current  will  flow  through  the  shunt  in  the  reverse  direc- 
tion and  the  machine  will  " build  up"  with  reversed  polarity. 

A  shunt  machine  will  not  generate  at  all  if  rotated  in  the  wrong 
direction.  The  residual  magnetism  will  cause  a  small  voltage 
to  be  generated  in  the  reverse  direction.  This  will  force  current 
around  the  fields  in  the  wrong  direction,  reducing  the  residual 
magnetism  present,  and  the  voltage  will  quickly  drop  to  zero. 
Similar  considerations  apply  to  the  series  and  the  compound- 
wound  generators. 

It  has  been  previously  shown  that  the  shunt  machine  will 
operate  either  as  a  generator  or  as  a  motor  with  the  same  direc- 
tion of  rotation.  The  same  is  true  of  the  compound  machine. 
When  the  machine  changes  from  a  generator  to  a  motor,  the 
current  in  both  the  armature  and  the  series  field  reverses.  If, 
therefore,  the  machine  operates  as  a  cumulatively  compounded 
generator,  it  will  be  a  differentially  compounded  motor.  Since 
the  latter  is  rarely  used,  if  we  wish  to  use  a  compound  generator 
as  a  motor,  it  is  generally  necessary  to  reverse  the  connections 
of  its  series  field. 

The  case  is  different  with  the  series  machine.  As  seen  from 
Fig.  41,  with  a  given  connection  and  direction  of  rotation,  it 
will  never  act  as  a  generator.  The  direction  of  the  back  e.m.f. 
is  opposed  to  the  current  as  a  motor.  If  an  attempt  is  made  to 
pass  current  in  the  same  direction  as  the  e.m.f.,  the  current  of 
the  series  field  will  be  reversed  and  consequently  the  magnetism 
of  the  field  will  be  rapidly  reduced  to  zero.  The  same  considera- 
tions will  apply  if  we  start  with  the  opposite  direction  of  current 
flow.  It  is  then  apparent  that  to  act  as  a  generator,  the  series 
machine  must  rotate  in  the  opposite  direction  to  its  rotation  as  a 
motor,  or  else  the  connections  of  its  armature  or  field  must  be 
reversed. 

PROBLEMS 

24.  A  certain  d.-c.  shunt- wound  motor  operating  at  230  volts  has  an  arma- 
ture resistance  of  0.03  ohm.  If  driven  by  outside  power  at  a  speed  of  900 


CHARACTERISTICS  OF  MOTOR*  73 

r.p.m.  the  machine  takes  no  armature  current  from  the  line  although  con- 
nected to  it.  What  will  be  its  speed  when  taking  150  amp.  armature  current 
as  a  motor?  What  at  75  amp.?  The  effect  of  armature  reaction  may  be 
neglected  in  the  above. 

26.  What  will  be  the  speed  of  the  same  machine  when  acting  as  a  generator 
and  delivering  the  above  currents,  the  field  current  being  assumed  to  remain 
constant? 

26.  A  230  volt  d.-c.  shunt-wound  motor  when  running  light,  i.e.,  with  no 
load  except  the  losses  in  the  armature  takes  an  armature  current  of  10  amp. 
and  rotates  at  a  speed  of  600  r.p.m.     What  will  be  its  speed  when  the  output 
is  50  hp.?     The  loss  in  the  field  may  be  neglected  and  the  resistance  of  the 
armature  taken  as  0.03  ohm. 

27.  If  the  armature  of  the  foregoing  machine  were  blocked  so  that  it 
could  not  rotate,  what  would  be  the  armature  current  when  full  voltage  was 
applied?     If  the  normal  current  of  the  machine  is  200  amp.  how  many  times 
full-load  torque  will  the  above  machine  develop  under  the  above  circum- 
stances?    (The  effect  of  armature  reaction  would  greatly  reduce  this  but 
may  be  neglected  in  solving  the  problem.) 

28.  At  standstill  the  above  machine  would  develop  zero  power.     It  can 
be  readily  shown  that  the  maximum  power  is  developed  (neglecting  friction 
and  hysteresis)  when  the  machine  is  rotating  and  taking  half  of  the  locked 
current.     With  this  current  what  is  the  input?     What  is  the  armature 
copper  loss?     Neglecting  all  other  losses,  what  is  the  output?     What  is  the 
efficiency?     What  is  the  torque  in  terms  of  the  full-load  torque? 

29.  A  certain  motor  has  an   armature   resistance   of   0.05    ohm.     The 
applied  e.m.f .  is  230  volts.     The  full-load  speed  with  50  amp.  in  the  armature 
is  1200  r.p.m.     At  what  speed  would  the  motor  have  to  run  to  take  zero 
current  from  the  line?     If  the  applied  e.m.f.  is  reduced  10  per  cent,  what  will 
be  the  speed  at  which  the  armature  current  is  zero,  it  being  assumed  that 
the  field  is  unsaturated  so  that  the  change  of  flux  is  proportional  to  the 
change  of  voltage?     What  will  be  the  full-load  speed? 

30.  What  will  be  the  corresponding  speeds  if  the  field  is  so  strongly  satu- 
rated that  there  is  practically  no  change  of  flux  with  a  10  per  cent,  change 
in  applied  e.m.f.? 

31.  What  will  be  the  corresponding  speeds  if  the  machine  is  separately 
excited? 

32.  A  certain  shunt-wound  motor  is  wound  to  operate  at  a  speed  of  600 
r.p.m.  with  zero  load  at  a  line  voltage  of  115.     At  what  speed  will  it  operate 
if  the  line  voltage  is  increased  to  230  and  enough  resistance  is  inserted  in  the 
shunt  field  circuit  so  that  the  field  current  is  the  same  as  before?     The 
machine  will  be  able  to  carry  the  same  current  in  the  armature  as  before. 
If  the  original  rating  was  25  hp.,  what  will  be  the  new  rating? 


CHAPTER  VI 


ACCESSORY  APPARATUS 

67.  Starting  Rheostats,  Series  Motors. — It  is  evident  from  a 
consideration  of  Fig.  43  that  any  of  the  ordinary  types  of  motors, 
if  of  reasonable  size,  will  develop  a  very  great  starting  torque 
when  connected  directly  to  a  constant  potential  line.  The  motor, 
of  course,  takes  a  correspondingly  large  current.  The  enormous 
torque  would  be  liable  to  result  in  great  damage  to  the  connected 
machinery,  and  to  the  belts  or  gears  used  in  transmitting  the 
power.  The  large  current  would  also  cause  flashing  at  the  commu- 
tator and  possible  damage  to  the  motor  by  heating.  For  these 
reasons,  it  is  necessary  to  use  resistors  to  limit  the  starting  current 
with  all  except  the  smallest  motors. 


FIG.  44. 


FIG.  45. 


Figure  44  shows  the  connections  of  a  starting  rheostat  for  a 
series- wound  motor.  This  consists  merely  of  a  resistor  connected 
in  series  with  the  motor  and  means  for  cutting  out  the  resistance 
as  the  motor  speeds  up.  In  some  cases  a  mechanical  interlock 
may  be  provided  so  that  it  is  impossible  to  close  the  main  switch 
S  unless  all  of  the  resistance  is  in  circuit. 

68.  Starting  Rheostats  for  Shunt  Motors. — The  case  of  the 
shunt  or  compound  motor  is  somewhat  more  complicated.  The 
current  which  passes  through  the  shunt  field  winding  is  not 
affected  by  the  speed  of  rotation.  Moreover  this  current  is  al- 
ways small  compared  to  the  total  current  of  the  motor.  In 

74 


A  CCEtiSOR  Y  APPA RA  T  US 


75 


order  that  the  motor  should  start  promptly  and  with  the  mini- 
mum current  in  the  armature,  it  is  essential  that  the  field  should 
be  as  strong  as  possible.  Hence  it  is  necessary  that  the  connec- 
tions be  made  in  such  a  manner  that  the  shunt  field  is  of  full 
strength  at  all  times.  A  connection  which  will  accomplish  this 
is  shown  in  Fig.  45.  When  the  switch  S  is  closed,  the  shunt  field 
takes  its  full  current.  The  resistance  of  the  rheostat,  R,  is  such 
that  approximately  full-load  current  flows  through  the  armature. 
The  motor  having  full  shunt  current  and  full-load  current  in  the 
armature  develops  full-load  torque,  and  if  the  load  is  not  above 
normal,  will  start  at  once.  The  rheostat  handle  is  then  moved 
steadily  across  the  contact  unit  all  of  the  resistance  has  been  cut 
out  and  the  motor  is  operating  at  full  speed. 

The  foregoing  connection  is  perhaps  the  simplest  that  can  be 
made,  but  it  is  open  to  a  serious  objection.     The  proper  method 
of  stopping  the  above  motor  would  be  to  open  the  main  switch, 
wait    until    the   motor    ceased   to 
rotate  and  then  move  the  rheostat 
handle    to    the    " start"    position. 
If  instead  of  doing  this  the  opera- 
tor stops  the  motor  by  first  mov- 
ing   the    rheostat    handle    to   the 
"start"  position  and  then  opening 
the  main  switch,  the  result  will  be 
that  a  heavy  arc  will  be  drawn  at 
the   contacts  of  the  main  switch. 
This  is  due  to  the  large  voltage  in- 
duced in  the  field  on  account  of  the  sudden  dying  down  of  the 
magnetism.     Not  only  are  the  contacts  burned,  but  there  is 
grave  danger  of  puncturing  the  insulation  of  the  field  because  of 
the  high  induced  voltage. 

Both  of  these  dangers  are  avoided  by  using  the  connection 
shown  in  Fig.  46.  If  the  motor  is  stopped  by  moving  the 
starting  handle  to  the  "start"  position,  the  field  circuit  is  not 
broken,  and  the  armature  supplies  a  gradually  decreasing  current 
to  the  field,  the  machine  acting  for  a  time  as  a  generator  to  the 
extent  of  supplying  the  field  current.  When  the  motor  is  started 
by  moving  the  starting  arm  on  to  the  first  contact,  a  fraction  of  a 
second  is  required  for  the  field  to  attain  its  full  strength.  An 
appreciable  time,  therefore,  is  needed  for  the  motor  to  develop 
its  full  torque  after  the  contact  is  made.  This  is  a  slight 


FIG.  46. 


76        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


advantage  as  it  avoids  giving  a  blow-like  impulse  to  the  connected 
mechanism. 

69.  The  No-voltage  Release. — Figure  46  shows  a  small  electro- 
magnet Mt  connected  in  series  with  the  shunt  field.  This  serves 
to  hold  the  rheostat  arm  in  the  running  position  against  the 
pull  of  a  spring.  If  for  any  reason,  the  supply  of  power  to  the 
motor  is  interrupted,  the  motor  slows  down  and  ultimately  stops, 
the  field  current  falls  to  zero  and  the  magnet  M  releases  the  arm, 
which  then  returns  to  the  starting  position.  This  protects  the 
motor  from  injury  when  the  line  again  becomes  energized. 

In  Fig.  47  is  shown  a  perspective  view  of  two-motor  starters  of 
the  type  discussed.  The  construction  will  be  clear  from  the 
illustration. 


FIG.  47. 

70.  Protective  Apparatus. — It  is  essential  that  a  motor  or  other 
piece  of  electrical  apparatus  be  protected  from  overload.  The 
simplest  way  of  doing  this  is  to  include  in  the  line  supplying  the 
motor  a  piece  of  readily  fusible  metal.  This  is  so  proportioned 
that  if  a  current  capable  of  injuring  the  apparatus  passes  for  a 
considerable  time,  the  metal  strip  or  wire  (called  a  fuse)  will 
melt  and  break  the  circuit. 

It  is,  of  course,  essential  that  the  fuse  be  properly  protected  so 
that  when  it  melts  the  heated  metal  will  not  be  thrown  where  it 
may  ignite  combustible  material.  Formerly,  porcelain  blocks 
were  used  to  enclose  the  fuse.  These  were  not  entirely  safe,  and 
it  was  too  easy  for  a  workman  to  replace  a  blown  fuse  with  a  larger 
size  of  wire,  or  even  with  a  piece  of  iron  wire,  a  nail  or  anything 
else  that  happened  to  be  handy.  At  present  the  enclosed  fuse 


A CCEXSOR  Y  APPA RA  T  US 


77 


is  almost  universal.  The  fuse  itself  is  enclosed  in  a  tube,  and 
the  space  between  the  fuse  and  the  tube  is  packed  with  incom- 
bustible material.  The  arc  due  to  the  rupture  of  the  fuse  is  thus 
effectually  smothered.  It  is  not  easy  to  refill  these  fuses  and  the 
workman  (except  car  motormen)  does  not  usually  have  replacing 
fuses  available.  As  a  consequence  the  matter  is  reported  to  the 
responsible  person  and  necessary  measures  are  taken  to  prevent 
a  recurrence  of  the  overload. 

71.  Circuit  Breakers. — When  an  enclosed  fuse  burns  out,  the 
expense    of    replacement    is    appreciable.     Moreover,    there    is 


FIG.  48. 

always  a  delay  in  replacing  it  and  getting  the  machinery  in 
motion  again.  The  money  value  of  the  fuse  and  the  lost  output 
while  the  machinery  is  shut  down  may  be  considerable.  To  meet 
conditions  of  this  character,  the  circuit  breaker  is  well  adapted. 
Figure  48  shows  a  modern  single-pole  circuit  breaker.  The 
instrument  consists  essentially  of  a  switch  with  such  additions 
that  it  opens  automatically  when  a  certain  current  is  exceeded. 
Either  an  electromagnet  or  a  solenoid  is  connected  so  that  the 
entire  line  current  passes  through  it.  When  the  current  for 
which  it  is  set  is  exceeded,  an  iron  plunger  or  armature  is  lifted 
against  the  force  of  gravity  by  the  attraction  of  the  magnet.  As 
the  plunger  rises  it  strikes  and  releases  a  latch,  and  a  spring  then 


78        PRINCIPLED  OF  DYNAMO  ELECTRIC  MACHINERY 

quickly  opens  the  breaker.  As  the  armature  rises  it  approaches 
nearer  to  the  magnet;  hence  it  is  more  strongly  attracted  and  rises 
rapidly,  striking  a  strong  blow.  The  first  contact  when  the 
breaker  is  closed  and  the  last  as  it  opens  is  made  upon  renewable 
carbon  blocks.  Since  the  arc  due  to  the  opening  is  taken  upon 
these  blocks,  the  main  contacts  are  protected. 

PROBLEMS 

33.  In  the  case  of  a  certain  series-wound  motor  the  full-load  current  is 
50  amp.     The  voltage  is  230.     The  resistance  of  the  armature  is  0.08  ohm 
and  the  series  field  0.05  ohm.     What  must  be  the  resistance  of  the  starting 
box  in  order  that  the  starting  current  shall  be  125  per  cent,  of  the  full-load 
current? 

34.  What  would  be  the  desired  resistance  if  the  above  machine  were 
shunt  wound? 


CHAPTER  VII 
RATING  OF  MACHINES 

72.  Influence  of  Speed. — The  output  of  a  given  electric 
generator  or  motor  is  nearly  proportional  to  its  speed.  Thus,  to 
take  a  simple  case,  assume  a  separately  excited,  continuous- 
current  generator,  rated,  say,  at  100  kw.,  125  volts,  and  operated 
at  a  speed  of  100  r.p.m.  Such  machines  are  frequently  used 
direct-connected  to  Corliss  engines,  except  that  they  would 
rarely  be  separately  excited,  and  would  usually  be  compound 
wound.  If  the  same  generator  were  operated  at  a  speed  of  200 
r.p.m.  by  being  direct  connected  to  a  high-speed  engine,  it  would 
generate  twice  the  voltage,  or  250  volts.  Since  the  winding  has 
not  been  changed  it  would  be  capable  of  carrying  about  the  same 
current  and  would,  therefore,  rate  at  twice  the  output,  or  200  kw. 
It  would  not  be  safe  to  carry  this  principle  too  far  in  practice 
since  various  troubles  in  connection  with  sparking,  balance, 
strains  due  to  centrifugal  force,  etc.,  would  be  encountered.  It 
should  also  be  noted  that  the  shunt  winding  would  not  be  adapted 
to  the  higher  voltage,  although  it  could  be  used  by  providing 
sufficient  field  resistance. 

It  follows  from  the  foregoing  that  the  cheapest  and  lighest 
machines  can  be  produced  by  operating  at  a  high  speed,  and 
conversely,  machines  for  direct  connection  to  slow-speed  engines 
or  water  wheels  are  correspondingly  heavy  and  costly. 

The  speed  of  a  generator  is  usually  fixed  by  the  requirements 
of  its  prime  mover,  since  most  generators  are  direct-connected. 
The  speed  of  motors  is  sometimes  limited  in  the  same  way,  as,  for 
example,  when  they  are  direct-connected  to  centrifugal  pumps. 
Where  either  generators  or  motors  are  belted,  it  is  advisable  to 
use  the  highest  possible  speed,  other  things  being  equal,  on 
account  of  the  saving  in  first  cost  of  the  machines.  Nevertheless, 
excessive  speed  should  be  avoided  on  account  of  rapid  wear  on  the 
bearings  and  commutator,  too  much  noise,  vibration,  etc.  The 
action  of  the  belt  at  high  speeds  offers,  however,  a  still  more 
serious  objection  to  the  employment  of  too  high  speeds.  Centrifu- 

79 


80        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

gal  force  tends  to  lift  the  belt  from  the  pulley,  and  thus  to 
offset  the  effect  of  the  belt  tension.  On  this  account,  it  is  neces- 
sary to  limit  the  peripheral  speed  of  belts  to  a  value  of  about  5000 
ft.  per  minute.  This  means  that  if  excessive  speeds  were  at- 
tempted, the  diameter  of  the  pulley  would  have  to  be  small,  and 
the  length  would  have  to  be  correspondingly  great.  This  would 
soon  lead  to  impracticable  sizes  of  pulleys. 

73.  Heating. — The  speed  at  which  the  generator  or  motor  is  to 
operate  having  been  determined  in  accordance  with  the  foregoing 
principles,  the  other  factors  which  determine  the  rating  in 
kilowatts  or  horse  power  of  the  generator  or  motor  remain  to  be 
considered.  An  electric  machine  is  inherently  capable  of  carry- 
ing enormous  overloads.  Any  one  of  several  factors  may,  how- 
ever, be  the  limiting  cause  to  force  a  lower  rating  of  the  apparatus. 

The  limiting  factor  which  most  frequently  determines  the  rating 
is  heating.  There  are,  in  the  machine,  whether  it  be  a  generator 
or  motor,  several  sources  of  loss.  There  is  mechanical  friction 
of  the  journals  and  commutator  and  air  friction.  In  addition, 
there  is  a  loss  due  to  the  alternate  magnetization  and  demagnet- 
ization of  the  iron  of  the  armature.  These  losses  are  present 
whether  the  machine  is  carrying  load  or  not,  and  their  value  is 
not  seriously  changed  by  the  magnitude  of  the  load.  In  addition, 
when  the  machine  is  called  upon  to  carry  a  load,  there  is  an  I2R 
loss  in  the  windings  of  the  armature  and  the  series  field.  This 
loss  varies  in  proportion  to  the  square  of  the  current  the  machine 
is  carrying.  There  is  also  an  PR  loss  in  the  shunt  field.  This 
is  independent  of  the  load  in  a  shunt  motor,  but  may  either  in- 
crease or  decrease  slightly  in  the  case  of  a  compound-wound 
generator,  depending  upon  whether  or  not  the  machine  is  over- 
or  under-compounded. 

These  losses  cause  the  temperature  of  the  machine  to  rise  above 
that  of  the  surrounding  atmosphere.  The  rise  continues  until 
the  difference  of  temperature  is  such  that  the  heat  is  radiated  as 
fast  as  it  is  generated.  After  this  temperature  is  reached,  there 
is  no  further  rise  or  fall  in  temperature  unless  the  load  is  changed. 
A  small  machine  may  reach  this  steady  temperature  in  an  hour 
or  less,  while  a  very  large  machine,  may  require  24  hr.  or 
more. 

Experience  has  shown  that  for  the  usual  insulating  materials 
the  temperature  should  not  rise  higher  than  to  about  95°C. 
(203°F.).  The  room  temperature  in  hot  engine  rooms  may  be  as 


RATING  OF  MACHINES  81 

high  as  40°C.  (104°F.).  This  leaves  an  allowable  rise  above  the 
room  temperature  of  55°C.  (99°F.)>  and  this  is  the  figure  usually 
adopted.  The  temperature  is  frequently  measured  by  thermo- 
meters applied  to  the  outside  of  the  completed  machine.  Since 
the  temperature  at  some  points  in  the  interior  must  be  higher, 
the  (American  Institute  of  Electrical  Engineers)  rules  specify 
that  15°  be  added  to  the  thermometer  temperature.  This 
leaves  an  observed  rise  of  40°C.  A  temperature  of  125°C.  is 
allowable  if  the  machine  is  insulated  with  mica,  asbestos  or  other 
material  capable  of  resisting  high  temperature. 

If  a  machine  is  to  be  used  in  intermittent  duty,  the  rating  as 
far  as  the  heating  is  concerned  may  be  made  much  higher.  For 
example,  if  a  motor  were  to  be  applied  to  a  hoist  it  would  be  im- 
possible to  have  the  full  load  on  the  motor  all  of  the  time,  and 
the  heating  for  the  same  maximum  load  would  be  less.  Hence,  it 
would  be  allowable  to  rate  the  motor  at  a  higher  horse  power 
than  if  it  were  to  be  used  in  some  service  in  which  it  would  be 
subjected  to  continuous  load. 

Motors  for  the  electric  propulsion  of  cars  are  rated  upon  a 
somewhat  different  basis.  In  fact,  the  service  of  a  traction 
motor  is  of  such  a  character  that  a  horse-power  rating  means  little 
or  nothing.  The  motors  are  habitually  worked  far  above  their 
rating  for  a  short  time,  while  the  car  is  accelerating;  are  then  dis- 
connected from  the  line,  and  allowed  to  revolve  idly  while  the  car 
is  coasting  and  later  are  brought  to  rest  when  the  car  is  stopped 
by  the  brakes.  Moreover,  the  motor  is  cooled  to  a  large  extent 
by  the  rapid  current  of  air  past  it.  The  latest  railway  motors  are 
even  fitted  with  special  means  for  internal  ventilation.  In  view 
of  these  facts,  many  makers  assign  a  horse-power  rating  to  rail- 
way motors  only  under  protest,  if  at  all.  If  any  rating  is  given, 
it  is  usually  based  upon  a  rise  of  75°C.  in  1  hr.  on  a  block  test  in 
the  shop.  Of  course,  this  gives  little  information  as  to  what 
the  motor  will  accomplish  in  actual  service  under  the  car. 

There  are  three  standard  types  of  motor  construction;  open, 
semi-enclosed,  and  enclosed.  A  given  motor  will  have  a  lower 
rating  for  continuous  duty  if  built  semi-enclosed  and  a  still  lower 
one  if  entirely  enclosed.  For  this  reason,  enclosed  motors  are 
little  used  except  for  intermittent  service  and  where  protection 
against  moisture,  dust,  chemicals,  etc.,  is  a  factor. 

74.  Efficiency. — To  a  certain  extent,  the  point  of  best  efficiency 
may  be  taken  into  consideration  in  fixing  the  rating  of  a  motor 


82        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

or  generator.  Usually  this  is  not  the  determining  factor,  since 
the  efficiency  of  electrical  machinery  is  so  high  that  no  material 
gain  in  average  efficiency  could  be  expected  by  basing  the  rating 
upon  efficiency.  This  is  not  by  any  means  the  case  with  other 
types  of  mechanism.  Thus  the  rating  of  steam  engines  and 
boilers  is  almost  universally  given  as  the  output  at  the  point  of 
best  efficiency.  An  engine  or  boiler  can  usually  develop  twice 
its  rating  without  injury  or  greatly  increased  rate  of  deprecia- 
tion, but  the  pounds  of  coal  burned  per  horse-power  hour  will  be 
increased. 

75.  Sparking. — For  machines  used  in  intermittent  service 
(and  to  a  lesser  extent  for  those  used  for  steady  service),  the  com- 
mutation is  sometimes  the  determining  feature  in  assigning  the 
rating.  To  understand  this  fully  we  shall  have  to  consider  what 
happens  during  the  period  while  the  current  in  a  coil  is  being 
reversed. 

Referring  to  Figs.  16  and  17  it  will  be  recalled  that  the  current 
in  the  armature  of  a  continuous-current  machine  is  distributed  in 
a  number  of  bands.  Thus  under  the  north  poles,  all  the  currents 
may  be  flowing  away  from  the  observer  while  under  the  south 
poles,  they  are  flowing  toward  him.  It  is  evident  that  the  cur- 
rent in  any  one  conductor  must  flow  in  one  direction  as  long  as 
the  conductor  is  under  a  given  pole  and  that  it  must  suddenly 
reverse  its  direction  and  flow  in  the  opposite  direction  as  long  as 
the  conductor  is  under  the  following  pole.  The  reversal  takes 
place  while  the  coil  of  which  the  conductor  is  part,  is  short- 
circuited  by  reason  of  the  brush  connecting  together  the  two 
commutator  bars  to  which  the  coil  is  connected. 

The  curve  of  current  in  an  armature  conductor  of  a  direct- 
current  machine  is  represented  in  Fig.  49.  During  the  period 
AB  the  current  remains  constant.  At  the  time  B  the  brush 
begins  to  short-circuit  the  coil.  At  the  time  C  one  of  the  com- 
mutator bars  to  which  the  conductor  is  connected  passes  from 
under  the  brush.  The  current  must  then  be  the  same  as  that 
in  the  other  conductors  with  which  it  is  in  series  or  it  must 
assume  the  value  CG  equal  to  its  former  value  AF.  This 
process  must  be  repeated  each  time  the  conductor  moves  a 
distance  equal  to  a  pole  pitch. 

There  is  no  question  about  the  straight  portions  of  the  curve, 
namely,  the  portions  AB  and  CD.  The  portion  of  the  curve 
BC  may,  however,  differ  widely  from  that  shown  on  account  of 


RATING  OF  MACHINES  83 

various  causes.  The  form  shown  represents  practically  the  best 
possible  condition  of  commutation. 

Just  before  the  coil  undergoes  commutation  a  current  /  is 
circulating  in  it.  This  current  sets  up  a  small  stray  magnetic 
field  surrounding  itself  and  thus  requires  a  certain  amount  of 
energy  for  its  establishment.  This  energy  must  be  dissipated  and 
an  equal  field  built  up  in  the  opposite  direction  while  the  coil  is 
undergoing  commutation.  The  inherent  difficulty  of  doing  this 
leads  to  most  of  the  trouble  experienced  in  obtaining  satisfactory 
commutation. 

The  energy  stored  in  a  coil  of  the  armature  is  equal  to  J£ 
LI2  where  L  is  the  coefficient  of  inductance  (see  Art.  121)  and 
I  is  the  current  in  the  coil.  The  expression  is  exactly  similar 
to  that  giving  the  energy  stored  in  a  moving  body,  namely  J^ 


J 


Time 


MV2  where  M  is  the  mass  of  the  body  and  V  is  its  velocity.  To 
stop  the  current  and  start  it  in  the  opposite  direction  is  similar  to 
stopping  the  motion  of  a  moving  body  and  setting  it  in  motion 
at  the  same  speed  in  the  opposite  direction.  In  the  case  of  a 
moving  body,  if  the  motion  is  stopped  by  an  obstacle  in  its  path 
heat  will  be  generated.  This  may  not  be  apparent  in  the  case  of 
a  small  body  moving  at  moderate  speed,  but  is  very  evident 
in  the  blow  of  a  steam  hammer  or  the  impact  of  a  projectile. 
The  attempt  to  stop  the  electric  current  leads  to  a  similar  evolu- 
tion of  heat,  usually  manifesting  itself  in  the  form  of  a  spark. 

76.  Resistance  Commutation. — Figure  50  shows  a  diagram- 
matic representation  of  the  armature  and  coils  of  a  continuous 
current  machine.  The  coils  are  represented  as  of  very  short  span 
in  order  to  make  the  diagram  clearer.  It  will  be  understood  that 
the  two  conductors  of  a  coil  carrying  the  current  across  the  face 
of  the  armature  would  be  separated  by  approximately  the  dis- 
tance corresponding  to  one  pole  pitch.  Imagine  that  the  arma- 
ture is  at  rest  and  that  current  is  entering  at  the  brush  shown.  It 
will  divide  into  two  equal  parts  passing  respectively  to  the  right 


84 


PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


and  left.  These  currents  will  pass  through  the  windings  and 
finally  emerge  at  the  next  brushes  to  the  right  and  left  of  the  one 
shown.  Of  the  various  coils,  those  marked  a  and  e  will  carry 
the  full  current  of  the  winding,  i.e.,  half  the  current  passing  into 
the  brush.  Each  of  the  next  two  coils  b  and  d  will  carry  some- 
what less  current  since  some  of  the  current  will  pass  into  the 
winding  by  way  of  the  commutator  bars  1  and  4  and  this  current 
will  not  pass  through  the  conductors  b  and  d.  The  conductor 
c  when  situated  as  shown  will  carry  no  current. 

It  is  evident  that  if  we  were  to  cause  the  armature  to  revolve 
very  slowly,  and  were  to  plot  the  current  in  one  conductor,  that 
the  shape  of  the  current  curve  would  resemble  that  of  Fig.  49. 
Thus  we  should  have  a  gradual  rise  and  fall  of  the  current  and 


FIG.  50. 

excellent  commutation.  However  as  soon  as  the  motion  of  the 
armature  becomes  at  all  rapid,  another  factor  enters.  As 
previously  mentioned,  a  current  passing  through  an  inductive 
circuit  acts  like  a  body  in  motion  and  resists  being  stopped.  The 
consequence  is  that  we  do  not  have  zero  current  in  the  coil  c 
when  the  armature  is  in  motion.  If  the  motion  is  from  left  to 
right,  the  current  in  a  will  be  in  the  same  direction  as  that  in  the 
coils  a  and  6.  If  the  motion  is  rapid,  it  may  even  happen  that 
the  current  will  still  be  flowing  in  the  original  direction  in  the 
coil  d.  This  will  lead  to  sparking  since  when  the  coil  d  finally 
passes  to  the  position  occupied  by  E  (and  the  current  must  pass 
in  the  new  direction),  there  will  be  an  action  equivalent  to  trying 
to  set  a  body  in  rapid  motion  in  a  very  short  interval  of  time. 
To  do  this  the  force  applied  must  be  very  great.  Hence  a  very 
great  e.m.f.  must  be  applied  to  the  coil  to  effect  the  reversal  and 
to  start  the  current  in  the  new  direction.  This  e.m.f.  may  be 


RATING  OF  MACHINES  85 

enough  to  cause  the  current  to  "  spill  over,"  as  it  were,  at  the 
point  which  separates  the  two  commutator  bars,  thus  giving  rise 
to  sparking. 

The  use  of  carbon  or  graphite  brushes  greatly  assists  the  corn- 
mutating  action  because  such  brushes  have  a  far  higher  contact 
resistance  with  the  commutator  than  metallic  brushes.  Thus, 
when  the  coil  is  short-circuited  by  the  brush  the  current  dies 
down  to  zero  much  sooner  and  commutation  is  facilitated.  In 
fact  the  action  is  equivalent  to  operating  the  machine  at  a  slower 
speed,  thereby  giving  the  current  more  time  to  reverse. 

77.  Effect  of  Rocking  the  Brushes. — In  the  foregoing  it  was 
tacitly  assumed  that  no  e.m.f.  was  induced  in  the  coil  except  that 
due  to  the  flux  set  up  by  its  own  current.  It  will  be  evident, 
however,  that  it  is  possible  to  provide  a  magnetic  field  such  that 
an  e.m.f.  will  be  induced  in  the  conductors  undergoing  commuta- 
tion. If  this  e.m.f.  is  just  strong  enough  and  is  in  the  right  direc- 
tion, it  will  reverse  the  current  already  present  in  the  coil  and 
build  it  up  to  the  same  strength  in  the  opposite  direction.  This 
will  result  in  perfect  commutation,  since,  as  the  coil  leaves  the 
brush,  it  will  be  carrying  the  same  current  that  will  flow  through 
it  until  it  reaches  the  next  brush. 

This  may  be  accomplished  in  an  imperfect  way  in  a  generator 
by  rocking  the  brushes  forward  or  in  a  motor  by  rocking  them 
backward.  Forward  rocking  in  a  generator  is  required  since  it 
is  necessary  that  the  e.m.f.  generated  in  the  coil  be  in  the  reverse 
direction  to  that  which  it  has  been  generating.  It  is  therefore 
evident  that  the  coil  must  be  in  a  position  where  it  is  to  some 
extent  subject  to  the  influence  of  the  next  pole.  In  a  motor,  the 
reverse  will  apply  since  the  current  is  flowing  in  opposition  to  the 
e.m.f.  generated  in  the  armature,  and  the  brushes  must  be  rocked 
backward. 

It  will  be  apparent  that  this  is  a  very  simple  way  of 
meeting  the  difficulty,  but  it  is  subject  to  very  serious  limita- 
tions. First,  it  is  entirely  inapplicable  to  motors  which  have 
to  be  reversed,  since  the  lead  of  the  brushes  would  be  wrong  when 
the  motor  was  operating  in  the  reverse  direction;  second,  the  effect 
of  armature  distortion  must  be  considered.  In  the  shunt  ma- 
chine as  shown  in  Art.  42,  this  results  in  weakening  the  leading 
pole  of  a  generator  or  the  trailing  pole  of  a  motor.  It  is,  more- 
over, toward  these  poles  that  the  brushes  must  be  shifted  in  order 
to  assist  the  commutation.  Thus,  the  lines  of  magnetic  induction 


86 


PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


which  should  assist  commutation  are  weakened  as  the  load  on  the 
machine  is  increased.  This  is  exactly  the  reverse  of  the  action 
desired,  since  these  should  increase  in  proportion  as  the  current 
increases.  Hence  the  best  that  can  be  expected  from  this  form 
of  commutation  is  some  help  to  the  resistance  commutation 
previously  described.  With  the  series  machine,  the  case  is  not  so 
bad  since  the  strength  of  the  field  increases  as  the  current  in- 
creases. Very  fair  commutation  can,  therefore,  be  obtained  in 
this  way  in  series  machines.  Unfortunately  series  generators 
are  rarely  used,  and  practically  all  series  motors  are  employed 
in  service  where  it  is  essential  that  the  motor  shall  operate  in 
both  directions.  This  prohibits  the  shifting  of  the  brushes  and 
the  use  of  this  property  to  assist  commutation. 

78.  Commutating  Poles. — The  best  method  of  commutation 
requires  the  use  of  auxiliary  poles.  These  are  commonly  known 
as  commutating  poles  or  interpoles.  A  diagrammatic  repre- 


Fio.  51. 

sentation  of  a  dynamo  machine  using  such  poles  is  shown  in 
Fig.  51.  In  addition  to  the  main  poles,  small  auxiliary  poles 
are  provided  as  shown.  The  winding  of  the  main  poles  may  be 
shunt,  series  or  compound.  The  commutating  poles  are  always 
series  wound.  Their  width  need  be  only  sufficient  to  cover  the 
conductor  during  the  whole  period  of  commutation.  As  they 
are  in  series  with  the  armature,  the  strength  of  these  poles  will 
always  be  in  proportion  to  the  strength  of  the  current  in  the 
armature,  and  consequently  just  the  proper  strength  to  give 
correct  commutation. 

A  motor  provided  with  commutating  poles  has  its  brushes  set 
at  the  geometrical  neutral  point.  It  will  give  correct  commuta- 
tion operating  in  either  direction  since  to  reverse  the  motion  the 
current  in  the  armature,  and  consequently  that  in  the  series 
winding  on  the  commutating  poles,  is  reversed.  Moreover,  the 
commutation  will  be  correct  for  any  speed  because  as  the  speed 


RATING  OF  MACHINES 


87 


increases  the  difficulty  of  reversing  the  current  increases  but 
the  voltage  generated  in  the  coil  undergoing  commutation  by 
the  flux  from  the  interpole  also  increases  in  the  same  propor- 
tion. This  is  a  point  of  great  importance  in  adjustable  speed 
motors.  A  motor  with  properly  designed  commutating  poles 
will  usually  carry  many  times  full-load  current  without  sparking. 


FIG.  52. 

The  limit  is  generally  found  in  the  ability  of  the  brush  to  carry  the 
current  without  glowing.  Figure  52  shows  the  field  of  a  modern 
motor  equipped  with  interpoles.  Many  generators  are  also 
now  provided  with  commutating  poles.  In  fact  it  would  be 
impossible  otherwise  to  build  generators  with  satisfactory  com- 
mutation for  large  outputs  and  high  speed  particularly  in  turbine- 
driven  continuous-current  machines. 


CHAPTER  VIII 
EFFICIENCIES  AND  LOSSES 

79.  Efficiency. — The  efficiency  of  any  machine  is  denned  as 
the  output  divided  by  the  input.     The  output  and  input  are 
usually  measured  in  watts  or  in  horse  power,  i.e.,  in  terms  of 
power,  but  may  be  measured  equally  well  in  work  using  as  units, 
kilowatt   hours   or   horse-power   hours.      Both   experience   and 
reason  teach  us  that  this  ratio  can  not  be  greater  than  unity,  and 
in  fact  since  all  machines  contain  imperfections,  must  be  less 
than  unity.     Of  course,  it  is  understood  that  the  machine  at  the 
end  of  the  test  is  in  the  same  condition  as  at  the  start ;  that  is,  we 
exclude  such  experiments  as  taking  a  partially  charged  storage 
cell,  adding  a  small  amount  of  energy  to  it,  and  taking  out  far 
more  energy  than  was  put  in.     Obviously  the  cell  would  not  be 
in  the  same  condition  as  at  the  start,  and  the  process  would  not 
be  capable  of  continuous  repetition. 

80.  Methods  of  Determining  Efficiency.— The  Brake  Test.— 
In  determining  the  efficiency  of  any  mechanism,  there  are  two 
possible  methods  of  procedure.     The  most  obvious  is  to  measure 
directly  the  work  or  power  put  in  and  the  corresponding  amount 
of  work  or  power  taken  out.     In  a  gas  engine,  for  example,  the 
quantity  of  gas  consumed  during  an  hour  may  be  measured,  and 
from  a  knowledge  of  the  calorific  properties  of  the  gas  used,  the 
work  or  energy  put  into  the  engine  can  readily  be  computed.     At 
the  same  time,  the  power  output  can  be  measured  by  means  of  a 
prony  brake  or  similar  appliance.     The  product  of  the  power  and 
the  time,  will  give  the  work  performed  by  the  engine.     The  output 
so  obtained  divided  by  the  input  reduced  to  the  same  units  will 
give  the  efficiency. 

This  procedure  is  often  carried  out  and  is  fairly  accurate. 
However,  it  gives  little  information  regarding  the  way  in  which  the 
losses  occur  and  is  therefore  of  little  assistance  to  the  designer  of  the 
engine,  although  it  may  give  all  the  information  the  user  desires. 

81.  The  Stray  Power  Method. — Another  method  of  procedure 
is  based  upon  the  principle  of  the  conservation  of  energy,  namely, 
that  all  of  the  energy  which  goes  into  the  engine  must  reappear 
in  some  form  or  other.     A  part  of  this  appears  in  the  form  of 

88 


EFFICIENCIES  AND  LOSSES  89 

useful  work.  Another  part  is  wasted  in  friction  of  the  parts  of 
the  engine,  air  friction,  etc.  Another  large  part  is  wasted  in 
heating  the  exhaust  gas,  and  another  in  raising  the  temperature 
of  the  cooling  water  used  to  keep  the  cylinder  within  the  working 
temperature.  If  the  amount  of  work  wasted  during  the  given 
interval  in  these  ways  could  be  accurately  measured  and  this 
quantity  be  subtracted  from  the  work  put  into  the  engine  in  the 
same  period,  it  would  be  certain  that  all  of  the  remainder  ap- 
peared as  useful  work.  We  should  then  be  able  to  compute  the 
efficiency  and,  in  addition,  should  have  information  regarding  the 
magnitude  of  the  individual  sources  of  loss.  The  designer  would 
than  be  in  a  position  to  lessen  these  losses,  if  excessive,  in  his  next 
design. 

In  the  case  of  electrical  machinery  the  stray  power  method 
is  the  one  almost  universally  employed.  This  results  from 
reasons  of  convenience,  small  quantity  of  power  required,  and 
on  account  of  the  greater  accuracy  obtainable. 

Considering  the  last  reason  first,  it  may  appear  strange  that 
an  indirect  method  can  be  more  accurate  than  a  direct  one.  The 
condition  arises  from  the  high  efficiency  of  electric  machinery. 
Thus  a  large  motor  might  easily  have  an  efficiency  of  95  per  cent. 
If  the  output  and  the  input  are  measured  separately,  with  an 
error  of  1  per  cent,  in  each,  making  the  output  too  high  and  the 
input  too  low,  an  efficiency  of  approximately  97  per  cent,  would 
be  obtained  for  the  final  result.  If,  on  the  other  hand,  we  had 
measured  the  loss  and  made  a  corresponding  error  of  1  per  cent,  we 
should  have  obtained  a  loss  of  4.95  per  cent,  instead  of  5  per  cent. 
The  result  would  be  that  the  computed 'efficiency  would  be  95.05 
per  cent,  in  which  the  error  is  negligible.  At  the  same  time  by 
using  this  method  we  should  obtain  the  value  of  the  individual 
losses,  which  information  might  be  of  great  value. 

82.  Losses  in  Direct-current  Machines. — The  principal  losses 
in  a  direct-current  machine  have  already  been  mentioned.  We 
shall  here  treat  them  more  in  detail  and  also  study  the  methods 
of  measuring  them.  As  a  simple  example  consider  the  case  of  a 
shunt  motor  already  installed  in  a  factory  and  whose  efficiency 
is  to  be  determined.  The  connections  of  the  motor  to  the  line 
are  as  shown  in  Fig.  53.  This  is  the  ordinary  connection  of  a 
shunt  motor  except  that  the  instruments  have  been  added.  R 
is  the  starting  rheostat,  used  to  limit  the  current  in  the  armature 
of  the  motor  during  starting.  An  ammeter  and  a  voltmeter  should 


90        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

be  provided  and  connected  as  shown  by  the  full  lines.  The 
ammeter  should  be  capable  of  measuring  a  current  equal  to  about 
10  per  cent,  of  the  full-load  current  of  the  motor.  The  value  of 
the  latter  can  usually  be  found  stamped  on  the  name  plate.  The 
ammeter  should  be  short-circuited  during  the  process  of  starting 
the  motor  since  the  starting  current  with  a  commercial  starting 
box  will  be  approximately  equal  to  the  full-load  current  of  the 
motor  and  this  would  be  liable  to  injure  a  meter  capable  of 
measuring  only  one-tenth  of  this  current. 

As  soon  as  the  motor  is  running  at  full  speed  the  short  cir- 
cuit may  be  removed  from  around  the  ammeter,  and  the  reading 
will  be  within  the  limits  of  its  scale  unless  there  is  excessive  loss 
from  some  cause  or  other.  The  product  of  the  readings  of  the 


FIG.  53. 

voltmeter  and  that  of  the  ammeter  will  be  the  power  in  watts  ex- 
pended in  the  armature  while  the  motor  is  running  without  load. 
83.  Stray  Power  Loss. — The  power  shown  by  the  instruments 
is  expended  solely  in  keeping  the  motor  in  rotation.  A  part  of  it 
is  wasted  in  bearing  friction  and  air  friction.  The  greater  part  of 
the  remainder  is  expended  in  hysteresis  and  eddy  current  losses. 
If  we  consider  a  certain  small  portion  of  the  iron  of  the  armature 
it  is  evident  that  when  this  portion  is  under  a  north  pole  the 
lines  of  magnetic  force  will  pass  through  it  in  a  certain  direction. 
As  soon  as  it  has  passed  under  a  south  pole  the  lines  will  pass 
in  the  opposite  direction.  To  cause  this  repeated  reversal  of 
the  magnetism  of  the  iron,  requires  a  certain  amount  of  power. 
The  exact  amount  depends  upon  the  rapidity  of  the  reversals  of 
the  flux,  the  flux  density  in  the  iron  and  the  quality  of  the  iron. 


EFFICIENCIES  AND  LOSSES  91 

Besides  this,  there  is  a  loss  in  the  iron  due  to  the  formation  of 
eddy  currents;  that  is,  small  stray  currents  in  the  iron  of  the 
armature.  This  latter  loss  can  be  made  very  small  by  making  the 
laminations  thin  enough. 

In  a  shunt  motor,  all  of  these  losses  are  practically  constant, 
irrespective  of  the  load  on  the  motor,  and  together  constitute  the 
stray  power  loss  of  the  machine.  It  is  true  that  some  of  these 
losses  increase  slightly  with  the  load  while  others  decrease  but  to 
say  that  the  total  is  constant  is  near  enough  to  the  truth  for 
any  ordinary  test.  It  is  evident  that  the  bearing  loss  will  be 
greater  when  the  load  is  large,  particularly  if  the  machine  is 
belted.  With  a  direct-connected  machine,  there  may  be  little 
difference.  The  loss  due  to  air  friction  will  on  the  other  hand  be 
less,  since  the  motor  slows  down  somewhat  as  the  load  increases, 
and  a  loss  of  this  nature  varies  nearly  as  the  cube  of  the  speed. 
The  hysteresis  loss  will  be  nearly  constant  since  the  magnetic 
field  is  nearly  constant,  but  will  decrease  somewhat  as  the 
load  increases  on  account  of  the  slight  reduction  of  speed.  On 
the  other  hand,  the  distortion  of  the  magnetic  flux  under  load 
tends  to  increase  the  loss.  The  same  conclusion  applies  to  the 
eddy  current  loss. 

84.  Shunt  Field  Loss. — There  is  also  a  constant  loss  in  the 
shunt  field  circuit.     The  value  of  this  is  readily  obtained  by  shift- 
ing the  ammeter  from  the  armature  circuit  to  the  shunt  field 
circuit  as  shown  by  the  dotted  connections.     The  loss  will  be  the 
product  of  the  volts  at  the  terminals  of  the  shunt  field  times  the 
current  in  the  field.     The  voltmeter  connections  should  also  be 
shifted  to  the  positions  shown  by  the  dotted  lines  unless  the 
motor  is  running  at  full  speed  when  the  measurement  is  taken, 
i.e.,  unless  the  resistor  R  is  completely  cut  out.     If  this  is  the  case, 
the  reading  will  be  the  same  in  either  position. 

It  may  seem  feasible  to  obtain  both  the  shunt  field  loss  and  the 
stray  power  loss  with  one  reading  by  connecting  the  ammeter  in 
the  main  circuit  so  as  to  include  the  current  in  both  the  armature 
and  the  field  at  the  same  time.  This  is  entirely  allowable  unless 
the  separate  losses  are  required. 

85.  Armature    Copper    Loss. — To    determine   the    armature 
copper  loss  we  must  know  the  resistance  of  the  armature.     This 
is  readily  obtained  by  preventing  the  armature  from  rotating  and 
taking  a  reading  of  the  voltmeter  and  the  ammeter  when  con- 
nected as  shown  in  the  full  lines.     The  simplest  method  of  pre- 


92        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

venting  rotation  is  to  disconnect  the  shunt  field.  The  brushes 
must  be  on  or  near  the  neutral  point  as  otherwise  the  armature 
might  magnetize  the  field  by  armature  reaction  enough  to  set 
the  motor  in  motion.  The  simple  blocking  of  the  armature 
will  be  equally  effective  if  it  can  be  more  conveniently  done. 
Nearly  all  the  starting  resistance  should  be  in  circuit  while  this 
reading  is  being  taken,  and  care  should  be  taken  to  secure  the 
readings  within  about  half  a  minute,  as  the  starting  resistor  is 
not  sufficiently  heavy  to  stand  being  in  circuit  continuously.  It 
will  be  found  that  the  voltage  across  the  armature  terminals  is  very 
low,  rarely  more  than  5  per  cent,  of  the  normal  running  voltage 
of  the  machine  when  full-load  current  is  passed.  To  secure 
accurate  readings  it  is  therefore  advisable  to  use  a  low  reading 
voltmeter,  unless  the  original  voltmeter  has  a  separate  low  read- 
ing scale.  It  is  also  advisable  to  take  several  readings  with  say 
M>  ^2>  %  and  full-load  current  in  the  armature.  This  is  done 
because  the  resistance  will  be  found  to  vary  somewhat  as  the 
current  is  changed.  The  variation  is  in  the  contact  resistance  of 
the  carbon  brushes  on  the  commutator.  A  resistance  of  this 
character  has  a  tendency  to  vary  *  in versely  as  the  amount  of 
current  passing.  For  the  greatest  accuracy  the  resistance  should 
be  taken  while  the  armature  is  being  rotated  slowly  by  hand. 
Of  course  there  must  be  no  current  in  the  field  while  this  is  being 
done,  as  this  would  introduce  an  e.m.f.  due  to  the  cutting  of  the 
lines  of  force.  Once  the  armature  resistance  for  various  currents 
is  known,  the  loss  for  any  current  is  readily  obtained  by  multiply- 
ing the  square  of  the  current  by  the  resistance  corresponding  to 
that  current. 

The  stray  power  loss  of  the  armature  taken  in  the  manner 
just  explained  includes  an  PR  loss  in  the  armature  conductors, 
but  the  loss  due  to  this  current  is  so  small  that  it  may  be  neg- 
lected without  appreciable  error.  The  stray  power  loss  and  the 
armature  I2R  loss  are  of  nearly  the  same  magnitude  when  the 
machine  is  operating  under  full  load.  While  measuring  the  stray 
power,  the  armature  current  will  rarely  be  more  than  5  per  cent, 
of  the  full-load  current.  Since  the  copper  loss  is  proportional 
to  the  square  of  the  current,  it  will  be  reduced  to  0.25  per  cent, 
of  its  full-load  value.  Hence,  it  is  small  enough  to  be  neglected 
in  most  cases.  If  greater  accuracy  is  desired  it  is  very  easy  to 
compute  its  value  and  subtract  it  from  the  power  found  in  the 
stray  power  measurement. 


EFFICIENCIES  AND  LOSSES  93 

If  the  test  is  an  important  one  the  temperatures  of  the  windings 
at  the  time  the  resistances  are  measured  should  be  taken.  The 
resistances  of  the  windings  at  75°C.  should  be  computed  and 
used  in  obtaining  the  efficiency. 

86.  Calculation  of  Efficiency  of  a  Shunt  Motor. — All  of  the 
losses  of  the  machine  have  now  been  considered.  The  input 
may  be  taken  as  given  by  the  name  plate  rating  at  full  load.  Sub- 
tracting from  this  value  the  losses  as  determined  will  give  the 
output  in  watts.  This  is  readily  changed  to  horse  power  by  di- 
viding by  746  and  the  value  so  obtained  should  agree  closely  with 
the  horse-power  rating  of  the  machine. 

It  will  be  noticed  that  it  has  not  been  found  necessary  to  load 
the  machine  at  all  in  order  to  obtain  its  efficiency,  so  that  one 
may  well  inquire  how  it  is  known  that  the  machine  will  carry 
the  load  assumed  at  all.  All  the  power  that  goes  into  the 
machine  must  reappear  in  some  form  or  other.  If  all  of  this 
power  is  not  accounted  for  in  the  shape  of  losses,  the  remainder 
will  be  available  as  useful  power  at  the  shaft  of  the  motor.  It 
may  be  quite  true  that  the  machine  might  not  be  a  satisfactory 
machine  at  the  load  assumed,  that  is  it  might  spark  badly  or 
overheat.  To  determine  these  features  a  separate  investigation 
is  required.  This  is  carried  out  most  readily  by  actually  running 
the  machine  under  its  rated  load  for  a  sufficient  time  to  allow 
the  temperature  to  rise  to  its  highest  value,  and  at  the  same  time, 
observing  the  character  of  the  commutation. 

Although  the  computations  may  be  made  without  the  use  of 
a  formula  it  may  be  desirable  for  certain  purposes  to  express  the 
efficiency  by  means  of  a  formula  as  follows: 

EI-P-  EI8  -  Ia*Ra 
11  ~~  ~ET 

in  which     77   =  Efficiency. 

P  =  Stray  power. 

E  =  Terminal  voltage. 

I,  =  Shunt  field  current. 

I a  =  I  —  I8  =  Armature  current. 

Ra  =  Armature  resistance. 

/  =  Total  current,  i.e.,  line  current. 

An  actual  example  may  serve  to  make  this  statement  clearer. 
A  certain  motor  is  rated  at  25  hp.,  900  r.p.m.,  full-load  current 
97  amp.,  volts  220.  The  machine  is  shunt  wound.  Connected 


94:        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

as  shown  in  Fig.  53  and  running  at  full  speed  with  all  of  the 
starting  resistance  cut  out,  the  machine  required  3.6  amp.  in 
the  armature  at  a  pressure  of  220  volts.  With  the  ammeter 
transferred  to  the  shunt  field  circuit,  2.75  amp.  at  a  pressure  of 
220  volts  was  indicated.  With  a  higher  reading  ammeter,  and  a 
lower  reading  voltmeter  substituted  for  those  of  Fig.  53,  and  with 
the  starting  lever  on  the  first  notch,  a  current  of  100  amp.  passed 
through  the  armature  and  the  voltmeter  indicated  11.7  volts. 
The  armature  was  blocked  so  it  could  not  rotate.  The  com- 
putations are  as  follows: 

Resistance  of  armature  and  brushes,  11.7  -*•  100  =  0.117  ohms. 

Stray  power  loss,  3.6  X  220  =  792  watts. 

Shunt  field  loss,  2.75  X  220  =  605  watts. 

Armature  copper  loss  (97-2.7S)2  X  0.117  =                          1,040  watts. 

Total  losses,  2,437  watts. 

Input,  97  X  220  =  21,340  watts. 

Output  =  input  —  losses  =  18,903  watts. 

Output  in  horse  power  =  18,903  -f-  746  =  25.4  hp. 

Efficiency  =  output  -4-  input  =  88.5  per  cent. 

The  same  method  may  be  applied  to  any  other  load.  Thus, 
if  it  is  desired  to  know  the  efficiency  at  Y±,  %,  %,  ^,  and  1% 
load,  we  start  by  estimating  the  current  required  at  these  various 
loads.  It  is  known  from  experience  that  at  Y±  load,  the  efficiency 
of  a  well-designed  -motor  will  be  lower  than  at  full  load.  Conse- 
quently somewhat  more  than  one-fourth  of  full-load  current  will 
be  required,  say  in  this  case  26  amp.  It  is  not  essential  to  come 
very  close  to  the  exact  current.  If  on  completing  the  compu- 
tation it  is  found  that  the  assumed  current  gives  a  horse  power 
/too  far  from  the  value  sought,  we  can  readily  select  one  more 
liearly  correct  and  perform  the  computation  again.  Selecting 
50  amp.  for  J^  load,  73  amp.  for  %  load,  and  121  amp.  for  \y±  load, 
the  values  for  the  following  table  can  be  computed : 

Loads ^  Y2  H  %  \Y± 

Amperes  (estimated) 26  50  73  97  121 

Stray  power 792  792  792  792  792 

Shunt  loss 605  605  605  605  605 

Armature  copper  loss 63  261  577  1,040  1,636 

Total  loss 1,460  1,658  1,974  2,437  3,033 

Input 5,720  11,000  JUMMK)  21,340  26,650 

Output  in  watts 4,260  9,342  14,086  18,903  23,617 

Output  in  horse  power  ....  5.70  12.5  18.9  25.4  31.7 

Efficiency,  in  per  cent 74.5  84.8  87.6  88.5  88.5 


EFFICIENCIES  AND  LOSSES 


95 


87.  Performance  Curves. — The  foregoing  figures  are  embodied 
in  the  curves  of  Fig.  54.  These  curves  can  be  used  in  various  ways. 
Thus,  suppose  the  motor  from  which  these  data  were  taken  is 
belted  to  a  line  shaft,  and  it  is  found  that  the  normal  current 
taken  by  the  motor  is  85  amp.  An  inspection  of  the  curve 
will  show  at  once  that  the  motor  is  developing  an  output  of  22 
hp.  Another  reading  taken  when  no  machines  are  connected  to 
the  line  may  show  that  a  current  of  60  amp.,  corresponding  to 
15.2  hp.  is  required.  These  results  will  at  once  suggest  the 
probability  that  more  efficient  operation  of  the  factory  can  be 
obtained  by  a  rearrangement  of  the  shafting  or  machines,  since  the 


10  12  14  16  18  20  22  24  26  28  30 

Output  in  H.P.  H.P. 

FlG.  54. 

power  required  to  operate  the  shafting  alone  is  69  per  cent,  of  the 
power  needed  for  the  operation  of  the  shafting  and  machines. 
So  valuable  are  tests  of  this  character  that  in  some  places  graphic 
recording  meters  are  installed  in  connection  with  important 
motors,  in  order  that  a  continuous  record  of  the  conditions  of 
operation  may  be  obtained. 

88.  Efficiency  of  a  Generator. — In  a  very  similar  manner,  the 
efficiency  of  a  generator  can  be  obtained.  The  stray-power  loss 
can  be  obtained  as  for  a  shunt  motor,  namely  by  running  the 
machine  from  some  other  source  of  electric  power  as  a  shunt 
motor  under  no  load.  The  stray-power  loss  so  obtained  may  be 
considered  as  constant  if  the  machine  is  shunt  wound  or  flat- 


96        PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

compounded.  If  over-compounded,  the  stray  power  should  be 
corrected  in  proportion  to  the  voltage  generated.  The  results 
so  obtained  will  not  be  strictly  correct,  but  will  be  close  enough 
for  ordinary  purposes.  The  shunt  loss  may  be  obtained  in  the 
same  manner  as  before.  If  the  terminal  voltage  of  the  machine 
varies,  the  shunt  loss  must  be  corrected  in  proportion  to  the 
square  of  the  voltage.  The  armature  and  brush  resistance  may 
be  obtained  in  the  same  way  as  for  the  shunt  motor.  The  resist- 
ance of  the  series  field  may  be  determined  separately,  or  the  volt- 
meter may  be  applied  outside  of  the  series  field  terminals,  in 
which  case  the  resistance  of  the  armature,  brushes  and  series 
field  may  be  obtained  with  the  one  measurement.  The  output 
should  be  taken  from  the  name  plate  and  the  losses  added  to 
it  in  order  to  obtain  the  input.  The  ratio  of  these  two  will  be 
the  efficiency  at  full  load. 

The  curves  of  Fig.  54  show  that  the  maximum  efficiency  occurs 
at  slightly  over  full  load.  This  would  be  an  economical  motor  if 
it  were  to  operate  at  practically  full  load  all  the  time.  In  the 
case  of  a  motor  in  which  the  load  is  variable  and  frequently  drops 
to  a  low  value,  it  would  be  preferable  to  have  the  maximum  effi- 
ciency occur  at  about  three-fourths  of  full  load.  This  would  give 
a  better  average  efficiency  for  the  range  of  work  performed. 
The  curve  will  also  show  the  inadvisability  of  using  a  large  motor 
to  carry  only  a  small  load.  Not  only  will  such  a  motor  be  more 
costly,  but  the  average  efficiency  will  be  lower  than  that  of  a  motor 
of  such  proper  capacity. 

89.  Change  of  Efficiency  with  Speed. — In  general,  motors  of 
high  or  moderate  speed  will  be  cheaper  in  first  cost  and  more 
efficient  than  those  of  low  speed.  Thus,  if  the  foregoing  motor 
had  been  operated  at  450  r.p.m.  instead  of  900,  its  rating  would 
have  fallen  to  about  12%  hp.  The  first  cost  would  have  been 
nearly  the  same,  about  the  only  saving  being  in  the  starting  box. 
The  copper  losses  in  the  armature  and  in  the  shunt  field  would 
be  the  same.  The  stray-power  loss  would  be  less,  perhaps  one- 
half  as  much,  at  the  lower  speed.  At  full  load,  the  total  losses 
would  become  1040  +  605  +  396  =  2041  watts.  The  input  would 
be  half  as  great  as  before  or  10,650  watts.  Subtracting  the  losses, 
leaves  an  output  of  8609  watts  (11.54  hp.  and  the  efficiency  is 
8609  -^  10,650  =  0.8083  or  80.83  per  cent.  Thus  the  efficiency 
is  decidedly  lower  at  the  lower  speed.  The  heating  will  be  nearly 
the  same  as  before.  It  is  true  that  the  losses  are  somewhat  less, 


EFFICIENCIES  AND  LOSSES  97 

but  on  the  other  hand  the  armature  is  not  revolving  so  fast,  and 
the  opportunities  for  radiation  are  therefore  not  so  good.  In 
practice  the  motor  would  undoubtedly  be  rated  at  12J^  hp. 
or  a  little  larger  load  than  that  assumed. 

A  similar  analysis  applied  to  generators  would  show  that  they 
also  are  lower  in  first  cost  and  higher  in  efficiency  at  high  speeds 
than  at  low  ones.  This  accounts  in  a  measure  for  the  success  of 
the  high-speed  turbo-alternator. 

PROBLEMS 

35.  A  certain  seiies-wound  motor  operating  at  75  volts  and  30  amp.  has 
a  speed  of  914  r.p.m.     The  machine  exerts  a  pull  of  10  Ib.  6  oz.  at  the  end 
of  a  brake  beam  17%  in.  long.     What  is  the  horse-power  output  of  the 
motor?     What  is  the  output  in  kilowatts?     What  is  the  efficiency  of  the 
motor? 

36.  In  determining  the  efficiency  of  a  shunt-wound  motor  the  following 
data  were  obtained.     With  the  motor  stationary,  the  current  through  the 
armature  was  adjusted  by  means  of  a  rheostat  to  100  amp.     The  drop 
across  the  brushes  was  6.2  volts.     With  no  load  the  machine  had  a  speed  of 
1200  r.p.ni.  and  took  a  current  of  5.1  amp.  through  the  armature  and  a  shunt 
field  current  of  3.5  amp.,  the  line  voltage  being  230.     For  inputs  to  the 
motor  of  25,  50,  75,  100  and  125  amp.  compute  the  stray  power  loss,  the 
armature  copper  loss,  the  field  copper  loss,  the  outputs  in  kilowatts,  the 
horse-power  outputs,  the  torques  in  foot-pounds  and  the  efficiencies.     Ar- 
range the  results  in  the  form  of  a  table  like  that  on  page  95. 

37.  The  foregoing  machine  has  four  poles  and  the  armature  is  lap  wound. 
The  armature  is  reconnected  with  a  wave  winding,  using  the  same  armature 
coils.     This  has  the  effect  of  reducing  the  paths  through  the  armature  from 
four  to  two.     The  field  is  not  altered.     What  is  the  resistance  of  the  rewound 
armature?     At  what  speed  will  the  armature  take  no  current  from  the  line? 
What  will  be  the  stray  power  loss  ?  .  (This  loss  may  be  taken  as  being  approxi- 
mately   proportional    to    the    no-load    speed.)     Compute    the    foregoing 
quantities  for  the  rewound  motor  for  currents  of  12.5,  25,  37.5,  50  and  62.5 
amp.     (These  currents  give  approximately  the  same  current  in  each  con- 
ductor of  the  armature  as  before.) 

38.  If  the  motor  as  originally  wound  was  rated  at  25  hp.,  what  is  the  new 
rating,  the  rating  in  each  case  being  based  upon  heating? 

39.  A  certain  10  hp.  115-volt  shunt  motor  with  a  speed  of  1200  r.p.m.  has 
a  field  loss  of  200  watts  and  a  stray  power  loss  of  450  watts.     The  resistance 
of  the  armature  is  0.02  ohm.     Find  the  value  of  the  armature  current  for 
which  the  efficiency  is  a  maximum  and  compute  the  efficiency  at  this  current. 
This  problem  is  based  upon  the  fact  that  the  efficiency  is  a  maximum  when 
the  fixed  and  the  variable  losses  are  equal. 


CHAPTER  IX 
DIRECT-CURRENT  MEASURING  INSTRUMENTS 

90.  Voltmeter  and  Ammeters. — In  continuous-current  work 
the  measurements  most  frequently  made  are  those  of  current 
and  e.m.f.     An  instrument  for  the  measurement  of  the  former 
is  called  an  ammeter;  for  the  latter,  a  voltmeter. 

Occasionally  very  crude  methods  serve  a  useful  purpose  in 
indicating  roughly  the  value  of  a  current  or1  an  e.m.f.  Thus,  it 
is  related  that  one  of  the  early  power  houses  had  a  comparatively 
small  copper  wire  in  series  with  each  of  the  generators.  When  the 
wire  became  red  hot  due  to  the  passage  of  the  current,  the  attend- 
ants knew  that  it  was  time  to  start  up  a  new  machine.  At  the 
same  period,  it  was  a  very  common  practice  to  use  an  incandescent 
lamp  as  a  crude  voltmeter,  the  attendant  estimating  the  voltage 
from  the  color  of  the  filament.  All  are  also  familiar  with  the  fact 
that  it  is  possible  to  detect  the  presence  of  a  moderate  voltage  by 
allowing  the  current  to  pass  through  the  body.  Naturally  this 
is  not  a  method  that  one  would  recommend  for  general  adoption. 

91.  The  D'Arsonval  Type  of  Instrument. — The  most  common 
type  of  direct  current  measuring  instrument  is  based  upon  the 
action  of  a  magnetic  field  upon  a  current.     Such  an  instrument, 
known  as  the  D'Arsonval  type,  is  illustrated  in  Fig.  55.     A  per- 
manent magnet  of  the  horse-shoe  type  is  provided  with  pole  pieces 
of  soft  iron,  and  to  make  the  magnetic  circuit  more  nearly  closed, 
a  cylinder  of  soft  iron  is  supported  inside  the  pole  pieces.     A  short 
air  gap  is  left  between  the  cylinder  and  the  pole  pieces  and  a  coil 
of  fine  wire  is  so  mounted  that  it  can  turn,  restrained  by  means  of 
one  or  more  fine  hair  springs.     The  current  is  led  to  the  coil  by 
suitable  flexible  conductors.     The  hair  spring  may  be  used  as  one 
of  these  conductors  or  two  springs  may  be  employed,  the  current 
being  passed  in  through  one  of  them  and  out  through  the  other. 

As  previously  noted,  when  a  current  is  passed  through  a  con- 
ductor lying  in  a  magnetic  field,  the  conductor  tends  to  move 
across  the  lines  of  induction.  In  the  instrument  described, 
it  is  evident  that  one  side  of  the  coil  will  be  urged  in  one  direction 


DIRECT-CURRENT  MEASURING  INSTRUMENTS 


99 


and  the  other  in  the  opposite  direction,  and  the  coil  will  tend  to 
turn  upon  its  axis.  Since  the  spring  restrains  the  motion,  the 
angle  through  which  the  coil  turns  will  be  dependent  upon  the 
strength  of  the  current.  By  providing  a  suitable  pointer  and 
scale,  it  is  possible  to  measure  the  current. 

In  order  that  the  instru- 
ment may  be  sensitive,  it  is 
necessary  that  the  coil  be 
very  light,  and,  therefore, 
wound  with  fine  wire.  More- 
over, it  would  be  impractic- 
able to  provide  flexible  leads 
for  any  but  a  very  small  cur- 
rent. Therefore  the  instru- 
ment can  not  be  used  as  it 
stands  for  any  but  small 
currents. 

This  condition  is  readily 
met  by  the  use  of  shunts. 
Suppose  that  we  had  an 
ammeter  with  an  extreme 
range  of  0.1  amp.  and  a  resistance  of  1.0  ohm.  If  we  connect 
in  parallel  with  it  as  shown  in  Fig.  56,  a  shunt  of  slightly  more 
than  0.001  ohm  (0.001001  ohm  to  be  exact),  the  current  will 
divide,  999  parts  passing  through  the  shunt  and  one  part 
through  the  instrument.  It  is  obvious  that  the  instrument  is 


FIG.  55. 


99.9  Amp. 

FIG.  56. 

now  capable  of  measuring  a  current  as  large  as  100  amp.  In 
a  similar  way  we  may  construct  as  many  shunts  as  we  wish  and 
an  ammeter  with  its  outfit  of  shunts  may  have  any  range  within 
reason.  In  many  cases  the  shunt  may  be  enclosed  in  the  same 
case  as  the  ammeter,  forming  a  self-contained  instrument  of 
large  range. 


100      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

92.  The  Voltmeter. — The  same  instrument  may  also  be  used  as 
a  voltmeter.  To  do  this  we  actually  measure  the  current  through 
a  known  resistance  and  calculate  the  corresponding  voltage.  By 
choosing  a  suitable  value  for  the  resistance,  the  calculation  becomes 
very  simple,  or  by  using  a  suitable  scale  the  reading  may  be  made 
direct.  Thus,  if  the  instrument  considered  be  connected  in  series 
with  999  ohms  (see  Fig.  57),  the  total  resistance  of  the  circuit 
will  be  1000  ohms.  If  we  should  apply  100  volts  to  this  circuit,  a 
current  of  0.1  amp.  would  flow.  This  we  have  assumed  will  give 
the  full  scale  deflection  of  the  instrument.  If  we  mark  the  point 
to  which  this  current  deflects  the  pointer  100  it  is  evident  that  the 
reading  will  be  direct. 

Similarly,  if  99  ohms  be  connected  in  series  with  the  instrument, 
its  maximum  reading  will  be  10  volts,  while  4999  ohms  would  give 
it  a  range  of  500  volts. 


AA/WWWV 

1  Ohm  999  Ohms 

FIG.  57. 

It  will  be  apparent  from  the  foregoing  that  one  instrument,  pro- 
vided with  suitable  shunts  and  resistors,  may  be  used  to  measure 
a  very  wide  range  of  currents  and  voltages. 

93.  The  Plunger  Type  of  Instrument. — In  the  foregoing  instru- 
ment a  coil  of  wire  is  caused  to  move,  due  to  the  action  between 
it  and  a  permanent  magnet.  Instead  of  using  this  construction, 
the  coil  may  be  fixed  in  position  and  the  permanent  magnet 
allowed  to  move.  However,  it  is  necessary  to  take  into  account 
the  action  of  the  magnetic  field  of  the  earth  upon  the  permanent 
magnet.  For  this  reason  it  is  customary  in  this  type  of  instru- 
ment to  use  a  piece  of  soft  iron  instead  of  the  permanent  magnet. 

In  one  construction  of  the  plunger  type,  the  coil  is  in  the  form 
of  a  solenoid  and  the  soft  iron  plunger  forming  the  core  is  pulled 
down  into  the  solenoid  by  the  action  of  the  current.  The  move- 
ment is  resisted  by  springs  or  by  the  action  of  gravity.  Such  an 
instrument  is  not  readily  portable,  and  a  large  amount  of  power 
is  required  on  account  of  the  weight  of  the  moving  parts.  For 
these  reasons,  this  form  of  instrument  is  not  much  used  at  the 
present  time. 

An  ingenious  modification  of  this  form  of  instrument  is  shown 


DIRECT-CURRENT  MEASURING  INSTRUMENTS       101 


in  Fig.  58.  The  coil  is  inclined  at  an  angle  of  approximately  45°C. 
with  the  horizontal.  The  "plunger"  consists  of  a  very  small 
piece  of  soft  iron,  and  it  is  also  arranged  at  an  angle  with  the  axis 
of  the  coil.  When  current  is  passed  through  the  solenoid,  the  soft 
iron  plunger  tends  to  place  itself  parallel  to  the  axis  of  the  coil. 
In  doing  this  it  rotates  upon  its  axis  and  carries  the  pointer  with 
it.  This  turning  is  resisted  by  a  spring.  This  form  of  instru- 
ment is  cheap  to  construct  and  gives  very  satisfactory  results  for 
ordinary  commercial  measurements.  It  requires  more  power  to 
operate  than  the  D'Arsonval  type;  is  not  so  sensitive  and  suffers 
the  disadvantage  that  the  scale  is  somewhat  crowded  at  both 
ends,  that  is,  the  deflections  are  not  proportional  to  the  currents 


FIG.  58. 

passing  through  the  coil.     It  may  be  used  for  alternating  as  well 
as  for  direct  currents. 

94.  Measurement   of  Power. — The   power  in   a  continuous- 
current  circuit  is  usually  measured  by  taking  the  product  of  the 
volts  and  the  amperes  in  the  circuit.     It  is  also  possible  to  use  a 
wattmeter  of  the  form  described  in  Chap.  XIII,  but  the  former 
method  is  usually  the  simpler. 

95.  Measurement  of  Work. — The  Watthour  Meter. — In  charg- 
ing for  direct-current  energy  it  is  necessary  that  we  have  an 
instrument  that  will  add  up  or  integrate  the  total  amount  of 
energy  used  during  a  given  time.     This  is  usually  accomplished 
by  means  of  a  small  continuous-current   motor,  connected  by 
gearing  to  a  counting  mechanism  which  records  the  revolutions 
of  the  meter.     The  motor  differs  from  the  common  type  of  power 
motor  in  that  usually  no  iron  is  used  in  either  the  field  or  the 


102      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

armature.     This  is  so  that  any  effect  due  to  the  saturation  of  the 
iron  may  be  avoided. 

The  armature  is  connected  as  a  shunt  across  the  line  and  the 
field  is  connected  in  series  with  the  line.  A  high  resistance  is 
connected  in  series  with  the  armature.  This  resistance  must  be 
great  enough  so  that  the  drop  across  it  will  be  large  in  comparison 
with  the  back  e.m.f.  of  the  motor;  that  is,  the  current  passing 


FIG.  59. 

through  the  armature  must  be  dependent  solely  upon  the  e.m.f. 
of  the  circuit  and  must  not  be  influenced  by  the  speed  of  the 
motor.  Under  these  circumstances  the  torque  of  the  motor  will 
be  proportional  to  the  e.m.f.  of  the  line  and  also  to  the  current 
flowing,  or  to  the  power  in  the  circuit. 

The  rotation  of  the  armature  is  resisted  by  a  disc,  usually  of 
aluminium,  mounted  on  the  shaft  and  rotating  within  the  field 
of  a  permanent  magnet.  This  produces  a  drag  or  counter-torque 
proportional  to  the  speed.  The  net  result  is  that  the  speed  of  the 
motor  is  proportional  to  the  power  in  the  circuit  and  conse- 
quently the  reading  of  the  counting  mechanism  in  a  given  period 


DIRECT-CURRENT  MEASURING  INSTRUMENTS         103 

is  proportional  to  the  product  of  the  power  and  the  time;  or  to  the 
energy.  As  will  appear  later,  this  same  form  of  meter  may  be 
used  on  alternating- current  circuits,  but  is  not  usually  so  used 
since  cheaper  and  possibly  more  satisfactory  forms  are  available 
for  such  circuits.  Figure  59  shows  the  construction  of  a  con- 
tinuous-current watthour  meter. 

PROBLEMS 

40.  A  certain  direct-current  D'Arsonval  type  instrument  is  intended  for 
use  both  as  an  ammeter  and  as  a  voltmeter.     The  scale  is  divided  into  100 
parts,  the  resistance  of  the  instrument  is  5  ohms  and  the  current  required 
to  produce  a  full-scale  deflection  is  10  milliamp.     (i.e.  0.010  amp.)     What 
resistance  must  be  used  in  series  with  this  instrument  in  order  that  it  may 
be  used  as  a  voltmeter,  giving  a  full-scale  deflection  with  1  volt?     With 
100  volts?     With  500  volts? 

41.  What  would  be  the  resistance  of  the  shunt  used  with  the  same  instru- 
ment if  it  is  to  give  a  full-scale  deflection  with  1  amp.?     With  10  amp.? 
With  1000  amp.? 

42.  An  incandescent  lamp  has  a  resistance  of  500  ohms  and  the  difference 
of  potential  across  its  terminals  is  100  volts.     A  voltmeter  having  a  resist- 
ance of  5000  ohms  is  connected  directly  across  the  terminals  of  the  lamp  and 
an  ammeter  whose  resistance  is  0.05  ohm  is  connected  so  as  to  measure  the 
current  going  to  both  the  lamp  and  voltmeter.    What  is  the  percentage  of  error 
in  the  determination  of  the  current  in  this  manner?     Of  the  voltage?     Of 
the  power?     What  would  be  the  corresponding  errors  if  one  terminal  of  the 
voltmeter  were  changed  so  that  the  current  to  supply  the  voltmeter  did  not 
go  through  the  ammeter?     Which  connection  is  preferable?     Which  would 
be  preferable  in  case  the  power  loss  in  a  very  low  resistance  were  to  be 
measured? 


CHAPTER  X 
ADJUSTABLE  SPEED  MOTORS 

96.  Adjustable  Speed  Motors. — An  adjustable  speed  motor  is 
one  whose  no-load  speed  may  be  adjusted  to  any  value  within 
a  certain  range  and  which  will  maintain  approximately  that  speed 
for  any  load  within  the  capacity  of  the  motor.     Motors  of  this 
type  are  frequently  required  for  driving  lathes,  drill  presses, 
planers  and  other  machine  tools.     When  an  ordinary  shunt  motor 
is  applied  to  drive  a  lathe,  it  is  generally  used  to  drive  the  counter- 
shaft and  the  speed  changes  can  be  obtained  in  the  ordinary  way 
by  means  of  cone  pulleys  and  back  gears.     This  method  of  opera- 
tion, however,  leaves  large  gaps  between  the  various  speeds,  and 
it  is  frequently  desirable  to  provide  a  means  for  obtaining  any 
speed  of  rotation  of  the  work  and  not  simply  a  few  speeds  differ- 
ing considerably  from  one  another.     This  need  is  supplied  by  the 
adjustable  speed  motor. 

With  a  motor  applied  as  described  to  a  standard  lathe,  the  range 
of  speed  control  would  not  need  to  be  great.  Probably  a  range 
of  one  to  one  and  one-half  would  be  sufficient.  However,  in 
the  case  of  this  or  other  machine  tools  it  sometimes  seems  de- 
sirable to  reduce  the  range  of  mechanical  speed  adjustment  and 
increase  the  electrical  speed  adjustment.  Therefore,  speed  ranges 
of  as  high  as  one  to  four  are  sometimes  called  for. 

97.  Shunt  Field   Control. — The  fundamental  equation  of  a 
direct-current  motor  is  (see  Article  58) : 

E  -  RI 
~^N~ 

It  will  be  evident  from  an  inspection  of  this  formula,  that  for  a 
given  value  of  the  current  /,  the  speed  may  be  changed  by  a  change 
in  any  one  of  the  other  factors.  The  external  voltage,  E',  the 
resistance  in  the  armature  circuit,  R]  the  number  of  conductors 
on  the  armature,  N;  or  the  flux  per  pole,  $1;  may  be  changed  and 
will  produce  a  corresponding  change  in  the  speed.  These  various 
methods  will  be  examined  separately. 

104 


ADJUSTABLE  SPEED  MOTORS 


105 


The  last  method,  varying  the  flux  of  the  motor,  is  the  one  most 
frequently  employed.  The  simplest  way  of  doing  this  is  to 
use  an  adjustable  rheostat  in  the  field  circuit.  The  connections 
are  shown  in  Fig.  60,  the  starting  box  being  omitted  for  the 
sake  of  simplicity.  Varying  the  resistance,  R,  changes  the 
current  flowing  through  the  shunt  field  circuit,  and  consequently 
the  strength  of  the  magnetic  field.  This  method  can  be  applied  to 
any  standard  shunt  motor  if  the  range  of  speed  adjustment  de- 
sired is  small,  say  10  or  15  per  cent.  The  cost  is  low  and  the  results 
are  entirely  satisfactory. 

When  larger  ranges  of  speed  are  desired,  it  generally  becomes 
necessary  to  adopt  special  motors.  This  necessity  arises  particu- 


FIG.  60. 

larly  from  the  difficulty  of  avoiding  sparking,  and  the  tendency 
of  such  a  motor  to  become  " unstable"  in  speed.  Both  of  these 
difficulties  are  the  result  of  armature  reaction.  It  has  been  shown 
that  the  armature  current  distorts  the  magnetic  field.  In  a 
motor  the  field  is  shifted  in  the  direction  opposite  to  the  rota- 
tion, and  at  the  same  time  is  weakened.  The  result  of  the  shift- 
ing is  that  the  neutral  point  is  no  longer  midway  between  the 
poles  but  is  shifted  backward.  Consequently  the  coil  under- 
going commutation  instead  of  being  in  a  zero  field  or  in  one  in  a 
direction  to  assist  commutation,  may  be  in  a  field  such  as  to 
oppose  commutation.  This  tendency  is  greatly  augmented  when 
the  main  field  is  weakened  to  secure  high  speed,  since,  on  account 
of  the  field  being  weak,  it  is  easier  for  the  armature  current  to  dis- 
tort it.  The  result  is  that  the  commutation  is  poor  at  high  speeds. 


106      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

To  keep  the  coils  undergoing  commutation  in  a  better  field,  the 
brushes  often  receive  a  backward  lead.  This,  as  already  pointed 
out,  is  not  a  complete  cure  and  at  the  same  time  it  introduces 
the  difficulty  that  the  armature  current,  in  addition  to  distorting 
the  flux,  also  weakens  it.  Thus,  an  increase  of  load  may  cause 
a  decrease  of  flux.  This  causes  a  decrease  of  the  back  e.m.f.  and 
a  corresponding  increase  of  current.  In  turn,  this  again  weakens 
the  field  and  leads  to  a  still  greater  current.  The  action  may 
readily  become  cumulative,  and  the  current  will  continue  to 
increase  until  the  fuses  blow  or  the  circuit  breaker  acts  and  opens 
the  circuit.  Before  this  takes  place,  the  motor  may  have 
attained  such  a  high  speed  that  the  wires  are  thrown  from  the 
armature  or  the  machine  is  otherwise  injured. 

98.  Use  of  Commutating  Poles. — Among  the  many  methods 
used  to  overcome  the  two  foregoing  defects,  the  use  of  commutat- 
ing  poles  is  perhaps  the  simplest.     These,  by  providing  a  separate 
field  for  commutation,  allow  effective  commutation  at  all  speeds, 
and  with  any  current  in  the  armature  within  reasonable  limits. 
At  the  same  time,  they  permit  or  even  require  the  setting  of  the 
brushes  at  the  geometrical  neutral  and  thus  the  possibility  that 
the  field  will  be  seriously  weakened  by  the  armature  current  is 
removed. 

99.  Methods  of  Changing  the  Magnetic  Circuit. — Besides  the 
method  of  weakening  the  field  by  using  a  rheostat  in  the  shunt 
circuit,  the  flux  can  also  be  weakened  by  changing  the  reluctance 
of  the  magnetic  circuit.     One  method  of  doing  this  is  to  form  the 
field  cores  with  a  sliding  plunger  as  part  of  the  pole.     The  con- 
struction of  the  Stow  adjustable  speed  motor  is  shown  in  Fig.  61. 
Mechanical  means  must  be  provided  to  withdraw  the  cores.     In 
the  motor  illustrated,  this  is  done  by  means  of  a  number  of 
bevel  gears  connected  together  by  shafts  and  all  operated  by 
means  of  a  hand  wheel. 

In  another  motor  which  depends  upon  somewhat  the  same 
principle,  the  armature  is  slightly  tapered  and  the  bore  of  the  field 
is  also  turned  to  the  same  taper.  Means  are  provided  to  slide 
the  armature  lengthwise.  This  results  in  an  increase  or  decrease 
of  the  air  gap,  and  a  corresponding  change  in  the  flux.  In  both 
of  these  methods  the  m.m.f.  of  the  main  field  is  not  altered. 
The  flux  is  consequently  not  shifted  to  the  same  degree  as  would 
be  the  case  with  a  plain  shunt  machine.  They  are  therefore  not 
so  liable  to  spark  or  be  unstable  in  speed  with  a  weakened  field. 


ADJUSTABLE  SPEED  MOTORS 


107 


The  objection  to  these  forms  is  that  they  involve  somewhat  com- 
plicated mechanical  structures. 

100.  Speed  Variation  by  Means  of  Resistance  in  the  Arma- 
ture Circuit. — The  connections  for  this  method  of  control  are 
shown  in  Fig.  62.  Referring  to  the  formula,  speed  variation  in 
this  case  is  secured  by  varying  the  resistance  R.  In  the  discussion 
of  the  formula  R  has  been  considered  as  the  resistance  of  the  arma- 
ture and  brushes.  Ordinarily  this  is  the  only  resistance  in  the 
armature  circuit.  In  this  method  of  control  additional  resistance 
is  purposely  introduced.  This  causes  the  motor  to  run  more 
slowly  in  order  that  there  may  be  sufficient  difference  between  the 
applied  and  the  back  e.m.f.  to  force  the  current  through  the  in- 


FIG.  61. 

creased  resistance.  The  result  is  that  the  speed  falls  off  more 
rapidly  with  increase  of  the  torque.  The  shape  of  the  speed 
torque  curve  depends  upon  the  amount  of  resistance  inserted  in 
the  armature  circuit.  Thus,  in  Fig.  63  the  highest  curve  repre- 
sents the  conditions  when  the  resistance  is  a  minimum,  i.e.,  when 
all  the  external  resistance  is  cut  out.  The  lower  curves  repre- 
sent the  effect  of  successively  greater  resistances.  It  will  be 
noted  that  the  speed  is  the  same  in  all  cases  at  zero  torque. 
Since  a  small  torque  is  required  to  overcome  the  resistance  of 
the  bearings,  the  air  friction  and  the  iron  losses,  the  motor 
running  with  no  load  will  not  quite  attain  these  speeds,  but  will 
run  at  some  such  speed  as  that  represented  by  the  intercepts 


108      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

with  the  dotted  line  AB.     The  distance  OA  is  the  torque  re- 
quired to  overcome  the  resistances  mentioned. 

This  method  of  control  is  seriously  defective  in  two  respects. 
In  the  first  place,  it  does  not  comply  with  the  definition  of  an  ad- 
justable speed  motor.  Thus,  if  the  motor  is  operating  with  such 
a  resistance  in  circuit  that  its  speed  torque  curve  is  represented 
by  No.  3,  and  is  acting  against  a  torque  OF,  such  that  its  speed  is 
FD',  if  the  torque  be  increased  to  OG,  its  speed  will  fall  toGE. 
This  may  be  decidedly  objectionable  in  certain  applications.  If 
the  motor  were  driving  a  lathe  operating  on  a  piece  of  such  shape 
that  the  tool  was  not  at  all  times  in  the  cut,  the  speed  would  in- 


FIG.  62. 

crease  to  a  great  extent  when  the  tool  ran  out  of  the  cut.  This 
would  lead  to  a  serious  shock  when  the  tool  again  began  to  cut 
the  metal. 

A  second  objection  is  that  the  efficiency  is  low  if  large  reduc- 
tions in  speed  are  secured.  If  the  speed  is  reduced  to  half 
of  normal,  the  current  required  for  a  given  torque  will  be  the 
same  as  though  the  motor  were  operating  at  full  speed.  The  use- 
ful work  done,  however,  will  be  only  half  as  great,  since  the  speed 
is  halved.  The  net  efficiency  can  not  therefore  be  more  than  50 
per  cent,  in  the  example  cited.  A  reduction  of  speed  to  one- 
fourth  of  normal  would  result  in  an  efficiency  of  less  than  25  per 
cent,  and  so  on. 

The  horse-power  output  of  the  motor  is  also  reduced  in  pro- 
portion to  the  speed.  The  maximum  torque  that  can  be  devel- 
oped remains  practically  the  same  no  matter  what  the  speed, 


ADJUSTABLE  SPEED  MOTORS 


109 


since  this  is  determined  by  the  current-carrying  capacity  of  the 
armature.  Since  the  speed  is  reduced,  the  capacity  in  horse 
power  is  reduced  in  the  same  proportion. 

The  two  foregoing  methods  are  often  applied  in  combination 
to  fan  motors.  The  rheostat  is  usually  so  arranged  that  moving 
a  lever  from  left  to  right  first  cuts  out  the  resistance  in  the 
armature  circuit.  After  all  this  is  out,  a  further  movement  of  the 
lever  cuts  in  the  field  resistance  thus  further  increasing  the  speed. 
Since  the  power  to  operate  a  fan  varies  about  as  the  cube  of  the 
speed,  the  power  required  at  low  speed  is  very  small  and  the  low 
efficiency  is  not  so  objectionable. 


Torque 

FIG.  63. 

101.  Motors  with  Two  Commutators. — Variation  of  the  num- 
ber of  conductors  in  series  is  most  easily  made  by  providing  a 
double  winding  on  the  armature.  Each  winding  is  connected  to 
its  own  commutator,  and  the  two  windings  are  entirely  insulated 
from  one  another.  Thus,  suppose  one  winding  is  provided  with 
100  conductors  in  series  and  the  other  with  160.  If  the  no-load 
speed  with  the  former  were  500  r.p.m.,  the  speed  with  the  other 
would  be  inversely  proportional  to  the  number  of  conductors  or 
500  X  100  -f-  160  =  313  r.p.m.  Moreover,  the  two  windings 
may  be  operated  in  series,  giving  the  equivalent  of  260  conductors 
or  in  opposition  giving  the  equivalent  of  60  conductors.  The 
respective  no-load  speeds  would  be  193  and  833  r.p.m.  Inter- 
mediate speeds  can  be  secured  by  the  use  of  resistance  in  the  shunt 


110      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


field.  The  efficiency  will  be  high  for  all  speeds,  and  the  normal 
horse-power  rating  of  the  motor  will  be  constant  no  matter  what 
the  speed.  This  method  is  little  used  at  the  present  time.  This 
condition  results  not  so  much  from  any  inherent  defect  of  the 
method,  as  from  the  fact  that  the  same  result  can  be  secured  with 
somewhat  simpler  apparatus  by  the  use  of  the  shunt  motor  with 
commutating  poles. 

102.  The  Multi-voltage  System. — We  have  still  to  discuss  the 
possibility  of  obtaining  speed  adjustment  by  changing  the 
applied  voltage,  E.  This  is  unfortunately  not  readily  done 
except  in  special  cases.  One  of  these  occurs  when  the  generator  is 
used  exclusively  to  furnish  current  for  a  single  motor.  This  case 


220 

V11V' 

nojv.                    J 

FIG.  64. 

will  be  considered  presently.  There  is  also  an  opportunity  to 
employ  this  method  when  three- wire  distribution  is  used  to 
supply  the  factory  where  the  motors  are  located.  In  this  case 
there  will  be  a  certain  voltage  between  one  of  the  wires  and  either 
of  the  others,  and  twice  this  voltage  between  the  other  two.  The 
connections  are  as  represented  in  Fig.  64.  The  shunt  field  is 
supplied  at  a  constant  voltage.  The  armature  is  so  connected 
to  a  single-pole,  double-throw  switch  that  it  may  be  connected 
to  the  neutral  wire  and  one  of  the  outside  wires,  or  to  the  two 
outside  wires.  In  the  example  shown,  the  voltage  applied  to  the 
armature  may  be  either  110  or  220  volts.  The  speed  would  be 
twice  as  great  with  the  latter  as  with  the  former.  This  method 
of  speed  variation  is  entirely  satisfactory  where  three-wire 
service  is  available.  It  may  be  combined  with  the  method  of 


ADJUSTABLE  SPEED  MOTORS 


111 


control  using  field  resistance  or  with  that  using  resistance  in  the 
armature  circuit. 

The  connections  of  the  shunt  field  should  not  be  changed  at  the 
same  time  as  the  armature  connections.  This  if  done  would 
result  in  weakening  the  field  current  in  the  same  proportion  as  the 
armature  voltage;  the  flux  would  also  be  changed  but  not  in  the 
same  proportion.  If  it  were  not  for  magnetic  saturation  the  field 
would  be  weakened  to  the  same  extent  as  the  armature  voltage 
and  the  speed  would  not  be  changed.  In  practice,  the  speed 
would  be  less  with  the  lower  voltage  but  not  half,  as  might  be 
expected. 

103.  The  Ward-Leonard  System.— In  Fig.  65  is  shown  a 
method  of  control  which  may  be  used  to  great  advantage  when  a 


FIG.  65. 

single  motor  (or  a  group  of  motors  all  used  for  the  same  purpose) 
takes  its  power  from  a  generator  used  to  supply  power  to  this 
motor  only.  The  main  generator  marked  G  in  the  diagram,  may 
be  driven  by  a  gas  or  steam  engine,  a  continuous-current  motor, 
an  alternating-current  motor,  either  single  phase  or  polyphase  or 
other  source  of  power.  The  driving  motor  whatever  its  type,  is 
usually  arranged  to  operate  at  practically  constant  speed. 

The  generator  G  and  the  exciter  E  are  driven  from  the  engine 
or  motor  by  direct  connection,  belting  or  in  any  other  suitable 
manner.  The  exciter  operates  at  constant  potential,  and  is 
therefore  usually  compound  wound.  If  a  continuous- current 
driving  motor  is  used,  this  exciter  may  be  dispensed  with, 
and  the  exciting  current  may  be  taken  directly  from  the  supply 
mains  (not  from  the  main  generator).  In  circuit  with  the 


112      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

field  of  the  generator  are  a  regulating  rheostat  R  and  a  re- 
versing switch  S.  The  former  serves  to  vary  the  field  current 
from  zero  to  full  strength,  and  the  latter  serves  to  reverse  this 
current.  To  start  the  motor  M,  the  field  circuit  of  the  generator 
is  closed  and  the  field  current  gradually  increased  from  zero  to  a 
strength  sufficient  to  give  the  speed  desired.  To  reverse  the 
motor,  the  field  strength  of  the  generator  is  reduced,  reversed 
and  strengthened  in  the  reverse  direction.  Thus  the  entire 
control  of  the  motor  is  accomplished  by  varying  the  small  field 
current  of  the  generator,  and  it  is  never  necessary  to  break  the 
large  current  flowing  between  the  generator  and  the  motor.  In 
order  to  handle  the  full- load  armature  current  without  sparking 
at  weak  field  strengths,  the  generator  is  usually  provided  with 
commutating  poles. 

Applications. — It  is  obvious  that  the  foregoing  system  is  far 
more  costly  than  direct  connection  between  the  prime  mover  and 
the  load.  Its  use  is  therefore  justifiable  only  in  special  applica- 
tions where  the  increased  flexibility  is  important  enough  to  offset 
the  added  cost.  Some  of  these  applications  will  be  discussed  in 
the  following  pages. 

104.  Rolling  Mills. — In  a  rolling  mill  there  is  always  a  sudden 
demand  for  great  power  when  the  billet  enters  the  rolls.  It  is 
also  frequently  necessary  that  the  rolls  be  promptly  reversed  in 
direction.  The  current  supply  is  commonly  three-phase  alternat- 
ing. A  three-phase  alternating-current  motor  is  not  well  adapted 
to  quick  reversals  of  direction  since  the  starting  torque  is  small. 
The  continuous- current  motor  on  the  other  hand  can  be  very 
quickly  and  easily  reversed.  The  writer  has  in  mind  the  case  of  a 
1200-hp.  rolling  mill  motor  which  is  brought  from  full  speed 
ahead  to  full  reverse  in  4  sec.  The  Ward-Leonard  system 
may  be  used  in  this  work.  A  three-phase  motor,  taking  its 
power  from  the  supply  system  may  drive  a  direct -current  genera- 
tor and  a  heavy  flywheel  mounted  on  the  same  shaft.  The 
direct- current  motor  which  drives  the  rolls  receives  its  power 
from  the  generator.  The  sudden  rush  of  power  required  when 
the  ingot  enters  the  rolls  is  supplied  largely  by  means  of  the 
flywheel.  This  slows  down  while  it  is  delivering  this  power  and  is 
subsequently  accelerated  by  the  alternating- current  motor.  Thus 
the  power  output  of  this  latter  is  made  more  nearly  constant  and 
a  smaller  motor  may  be  employed.  When  being  stopped,  the 
continuous- current  motor  returns  power  to  the  generator  and 


ADJUSTABLE  SPEED  MOTORS  113 

flywheel,  since  the  generator  field  is  weakened  at  this  time  and 
the  motor  voltage  is  consequently  higher  than  that  of  the 
generator.  This  results  in  a  large  power  saving. 

105.  Propulsion  of  Ships. — In  the  last  few  years,  the  applica- 
tion of  the  internal  combustion  engine  and  the  steam  turbine 
to  the  propulsion  of  ships  has  received  great  attention.     Both 
of   these   prime   movers   operate  most  economically  at  speeds 
considerably  above  the  most  efficient  speeds  of  the  screw  pro- 
peller.    This  is  particularly  the  case  with  the  turbine.     More- 
over,  the  turbine  is  absolutely  irreversible,  and  it  is  necessary 
to    provide    entirely   separate    turbines   for  reversing  the  ship. 
The  internal  combustion  engine  also  suffers  in  comparison  with 
the  steam  engine  in  regard  to  its  ability  to  reverse  promptly  and 
with  certainty,  and  in  its  ability  to  operate  at  low  rates  of  revolu- 
tion  while   maneuvering.     By  using   an   electrical    method   of 
transmitting  the  power  from  the  engine  to  the  propeller,  the 
speed  of  each  may  be  chosen  without  reference  to  that  of  the 
other  and  reversal  becomes  very  simple.     The  engine  would  be 
of   the   governed   type   operating   at    full    speed.     The   control 
elements  may  be  located  in  the  pilot  house,  thus  making  the 
transmission  of  signals  with  their  delay  and  possibility  of  mistake 
unnecessary. 

It  should,  however,  be  pointed  out  that  in  the  case  of  the 
turbine  ship,  an  alternating-current  generator  and  induction 
motors  would  probably  be  used,  at  least  in  the  larger  sizes,  since 
it  is  difficult  to  construct  very  large  direct- cur  rent  generators  to 
operate  at  turbine  speeds.  The  use  of  continuous-current  pro- 
pulsion is  therefore  limited  to  small  vessels. 

106.  Operation  of  Gas-electric  Cars. — Cars  operated  by  gaso- 
line or  oil  engines  are  finding  considerable  favor  at  the  present 
time.     They  are  of  use  as  local  cars  in  connection  with  trunk 
lines  and  as  independent  systems  when  the  frequency  of  opera- 
tion is  such  that  it  would  not  pay  to  install  electric  traction  with 
its  high  cost  for  the  overhead  conductor  or  the  third  rail.     The 
internal  combustion  engine  operates  best  at  nearly  a  constant 
speed.    It  has  no  starting  torque  and  consequently  provision  must 
be  made  so  that  it  may  be  in  operation  before  the  car  is  started. 
It  is  then  necessary  to  provide  some  means  of  connecting  the 
engine  to  the  wheels  and  varying  the  speed  ratio  between  them. 
.Mechanical  gearing  similar  to  that  used  on  automobiles  has 
been  employed  in  some  cases.     An  electric  connection  is,  how- 

8 


114      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

ever,  undoubtedly  more  flexible,  and  it  is  the  opinion  of  many 
builders  of  this  class  of  apparatus  that  it  is  also  more  reliable. 
For  this  purpose,  the  series  motor  is  preferable  to  the  shunt. 
Usually  two  or  four  motors  are  used.  This  is  done  so  that  more 
of  the  wheels  may  be  used  in  driving  the  car,  thus  enabling  the 
car  to  produce  a  greater  tractive  effort.  The  different  series 
motors  may  be  connected  in  parallel.  Reversing  the  direction 
of  the  voltage  of  the  generator  would  not  reverse  the  direction  of 
rotation  of  the  series  motors,  since  the  field  and  the  armatures 
would  be  reversed  at  the  same  time.  The  reversing  switch  in 
the  generator  field  is  therefore  omitted  and  instead  a  switch 


Motors 


FIG.  66. 

is  provided  to  reverse  the  series  fields  of  the  motors.  Un- 
fortunately, in  this  case  we  are  obliged  to  have  a  switch  in 
circuit  with  the  main  current,  but  the  controller  is  so  arranged 
that  this  switch  can  not  be  opened  until  the  field  circuit  of  the 
generator  is  broken.  There  is  therefore  no  current  flowing  in  this 
circuit  when  the  fields  are  reversed  and  consequently  no  burning 
of  the  contacts  can  occur  on  account  of  breaking  the  circuit. 
One  way  of  connecting  such  a  set  is  indicated  in  Fig.  66.  Pro- 
vision is  also  usually  made  so  that  the  motors  may  be  connected 
either  in  parallel  or  in  series.  This  is  done  so  that  the  motors 
may  be  operated  in  series  for  starting  or  at  low  speeds.  Only 
half  as  much  current  is  required  for  a  given  torque  with  two 
motors  in  series  as  with  the  same  motors  in  parallel. 

PROBLEMS 

43.  A  motor  connected  as  shown  in  Fig.  62  takes  a  current  of  100  amp. 
through  the  armature  at  a  pressure  of  250  volts  and  operates  with  no  external 


ADJUSTABLE  SPEED  MOTORS  115 

resistance  in  the  armature  circuit  at  a  speed  of  600  r.p.m.  giving  an  output 
of  27  hp.  If  the  resistance  of  its  armature  is  0.05  ohm,  how  much  resistance 
must  be  connected  in  series  with  it  in  order  that  the  speed  may  be  reduced 
to  300  r.p.m.,  the  current  remaining  the  same?  What  is  the  output  of  the 
motor  at  the  reduced  speed? 

44.  In  the  case  of  the  same  motor  with  the  armature  resistance  as  deter- 
mined in  circuit,  what  will  be  the  speed  if  the  load  is  reduced  so  that  the 
armature  current  falls  to  50  amp.?  What  if  it  is  increased  to  150  amp.? 
To  200  amp.? 

46.  A  motor  is  connected  as  shown  in  Fig.  64.  The  voltages  are  as  indi- 
cated. The  resistance  of  the  armature  is  0.12  ohm  and  the  armature  cur- 
rent is  50  amp.  If  the  speed  is  700  r.p.m.  when  the  armature  is  connected 
to  the  110- volt  circuit,  what  will  be  the  speed  when  it  is  connected  to  the 
220-volt  mains?  What  would  be  the  approximate  speed  if  both  the  arma- 
ture and  the  field  were  connected  to  the  110-volt  circuit?  Can  this  be  stated 
definitely  with  the  data  at  hand?  Is  this  a  usual  connection? 

46.  If  the  stray  power  loss  of  the  motor  in  the  above  problem  is  500 
watts  at  110  volts  or  1000  watts  at  220  volts  and  the  resistance  of  the 
shunt  field  is  150  ohms,  what  is  the  efficiency  at  110  volts  and  100  amperes 
armature  current?  At  220  volts  and  the  same  current? 


CHAPTER  XI 
ALTERNATING  CURRENTS 

107.  General  Principles. — In  studying  the  principles  ot 
alternating  currents,  it  is  highly  desirable  to  keep  clearly  in 
mind  the  analogy  between  the  laws  governing  the  action  of 
electric  currents,  and  those  applying  to  tangible  matter.  These 
laws  are  almost  the  same  in  the  two  cases.  Where  there  are 
differences,  it  will  usually  be  found,  contrary  to  the  general 
impression,  that  the  laws  governing  ordinary  matter  are  more 
complex  than  those  of  electricity.  In  fact;  paradoxical  as  it 
may  sound,  the  simplicity  of  the  laws  of  electricity  is  what  causes 

JP\ Pipe  Carrying  Water iPg 

I          I  '  I  I 

I  I 

1  t 

\E\  Wire  Carrying  Current  >E» 


FIG.  67. 

the  subject  to  be  difficult;  that  is,  this  simplicity  has  led  electrical 
engineers  to  attempt  mathematical  investigations  of  considerable 
complexity.  The  same  investigations  might  be  applied  to  many 
questions  in  mechanical  engineering,  but  the  fact  that  at  many 
stages  of  the  process  one  would  have  to  say,  "this  is  only  approxi- 
mately so,"  would  rob  the  result  of  much,  if  not  all,  of  its  value. 
As  a  simple  illustration,  consider  the  electric  circuit  and  the 
corresponding  water  circuit  of  Fig.  67.  Let  the  electrical  pressures 
at  the  points  A  and  B  be  respectively  E\  and  Ez,  and  let  E\  — 
EZ  =  E.  We  may  then  write  the  expression 

I=E- 
R 

where  R  is  the  resistance  of  the  circuit  and  7  is  the  current. 

Similarly,  in  the  hydraulic  circuit,  Pi  —  P2  =  P  and  we  have 

p 
C  =  D  where  as  before,  R  is  the  hydraulic  resistance  of  the  part 

116 


ALTERNATING  CURRENTS  117 

of  the  circuit  between  A  and  B,  and  C  is  the  " current"  of  water. 
By  " current"  is  meant  the  "rate  of  flow,"  i.e.,  the  gallons  per 
second  in  the  case  of  water,  or  the  coulombs  per  second  in  the  case 
of  electricity.  In  electricity,  this  unit  is  named  the  ampere.  In 
hydraulics  it  has  no  name,  and  must  be  designated  in  the  some- 
what awkward  manner  used  above. 

In  the  case  of  the  electric  circuit,  the  equation  is  exact;  that  is, 
R  is  a  true  constant,  and  does  not  vary  at  all  with  the  current. 
In  the  hydraulic  analogy,  however,  the  equation  is  nothing  more 
than  an  approximation,  and  a  correction  would  have  to  be  used 
if  an  attempt  were  made  to  apply  it  to  a  wide  range  of  pressures. 
In  other  words  the  resistance  R  is  not  a  constant,  but  is  a  vari- 
able and  a  function  of  C.  Many  other  examples  might  be  given, 
illustrating  the  fact  that  in  general,  the  electrical  phenomena 
are  the  simpler.  Occasionally,  it  is  true,  the  situation  is  re- 
versed, and  the  mechanical  problem  is  the  simpler.  These  cases 
will  be  pointed  out  in  their  proper  place. 

108.  Definition  of  an   Alternating   Current. — An   alternating 
current  is  one  in  which  the  direction  of  flow  is  rapidly  reversed. 
We  usually  add  to  this  the  proviso  that  the  current  shall  pass 
in  the  two  directions  following  the  same  law  of  change,  that  is, 
so  that  it  would  be  represented  by  the  same  curve  on  the  two  sides 
of  the  zero  axis.     For  example,  in  the  secondary  of  an  induction 
coil,  the  same  amount  of  electricity  passes  in  each  direction,  but 
in  one  direction,  that  corresponding  to  the  break,  the  current 
passes  in  the  form  of  a  violent  rush  of  short  duration;  while  at 
the  make,  the  same  amount  of  electricity  passes  but  the  current 
is  weaker  and  lasts  enough  longer  to  make  the  quantity  the  same. 
We  would,  therefore,  hardly  call  this  an  alternating  current,  as 
generally  understood. 

109.  Wave  Shape. — One  method  of  representing  an  alternating 
current  is  by  means  of  a  curve  as  shown  in  Fig.  68.     The  ab- 
scissae- are  the  times,  the  ordinates,  the  currents  at  the  corre- 
sponding times. 

The  wave  shown  in  Fig.  68  is  known  as  a  sine  wave.  This 
shape  is  the  one  aimed  at  in  all  alternating  machinery,  although, 
on  account  of  inaccuracies  in  workmanship,  the  necessity  of  pro- 
viding teeth  on  the  armature  surface,  distortions  introduced  in 
the  magnetic  flux  by  the  current  generated  and  other  factors, 
the  best  that  can  be  obtained  is  an  approximation.  In  Figs. 
69  and  70  several  waves  as  given  by  commercial  machines  are 


118      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

shown.  The  wave  shape  is  also  influenced  by  the  character  of 
the  circuit  through  which  the  current  is  passed.  In  general, 
if  reactance  is  in  the  circuit,  the  effect  is  to  make  the  wave  of 


FIG.  68. 


FIG.  69. 


FIG.  70. 


current  more  nearly  sinusoidal  than  the  wave  of  the  applied  e.m.f . 
If,  on  the  other  hand,  there  is  a  condenser  in  the  circuit,  any  ir- 
regularity will  be  increased.  These  effects  are  shown  in  Figs. 
71  and  72  respectively. 


ALTERNATING  CURRENTS 


119 


110.  Frequency. — By  a  cycle  we  mean  one  complete  set  of 
positive  and  negative  values  of  an  alternating  current.  The 
frequency  is  the  number  of  cycles  per  second.  Formerly, 
it  was  customary  to  designate  a  circuit  by  the  number  of  alter- 


E.M.F. 


Current 


FIG.  71. 


nations  per  minute,  an  alternation  being  half  of  a  cycle.  Thus 
60  cycles  would  correspond  to  7200  alternations;  25  cycles  to 
3000  alternations,  etc.  This  designation  is  rarely  used  at  the 
present  time. 


FIG.  72. 

The  frequencies  in  most  common  use  in  the  United  States  are 
60  and  25  cycles.  In  Europe,  the  frequencies  most  used  are  50 
and  25  cycles.  Formerly,  133  and  120  cycles  were  extensively 
employed.  These  give  good  results  when  used  for  lighting  only, 
but  are  less  suitable  for  power  development.  On  this  account, 


120      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


they  are  not  used  at  the  present  time,  except  in  old  installa- 
tions. Other  frequencies  occasionally  encountered  are  40, 
33,  30  and  15  cycles.  The  last  has  been  proposed  and  used  to  a 
slight  extent  in  the  electrification  of  railroads. 

Of  the  two  common  frequencies,  60  and  25  cycles,  the  former 
is  largely  used  for  lighting  and  most  of  the  smaller  power  applica- 
tions. The  latter  is  used  where  the  motors  on  the  system 
are  mostly  of  large  size,  and  particularly  if  a  large  part  of  the 
power  is  to  be  transformed  to  direct  current  by  means  of  rotary 
converters. 

111.  Construction  of  Sine  Curve. — As  before  stated,  the  sine 
wave  is  considered  the  standard  alternating-current  wave.  The 
reasons  for  this  choice  will  appear  gradually  as  we  progress.  It 
will  suffice  to  point  out  at  the  present  time  that  sinusoidal  motion 
d  •  


\ 


\s 


FIG.  73. 

(also  called  simple  harmonic  motion)  is  the  simplest  of  all  to-and- 
fro  motions.  The  motion  of  the  piston  of  a  steam  engine  if  the 
connecting  rod  is  extremely  long,  is  simple  harmonic.  So  also 
is  the  motion  of  a  pendulum,  if  the  decrease  in  the  amplitude  due 
to  the  friction  of  the  air  and  of  the  suspension  be  neglected.  The 
motion  of  a  weight  suspended  on  a  spring,  the  discharge  of  elec- 
tricity from  a  condenser  and  many  other  natural  phenomena,  also 
follow  the  same  law. 

The  method  of  constructing  a  sinusoidal  curve  is  shown  in 
Fig.  73.  The  point  c  is  supposed  to  be  rotating  around  the  circle 
in  a  counter-clockwise  direction  as  shown  with  a  uniform  angular 
velocity  of  co.  We  may  think  of  the  angle  9  as  increasing  with- 
out limit,  i.e.,  not  limited  to  360°,  and  we  then  have  the  relation 

ob  —  oc  sin  6  =  oc  sin  co£ 

and  we  say  that  the  point  b  executes  simple  harmonic  motion 
along  the  axis  ddf.  In  constructing  the  curve,  we  may  consider 
the  horizontal  distances  as  representing  either  angles  or  time, 


ALTERNATING  CURRENTS  121 

since  with  uniform  circular  motion,  the  one  is  proportional  to  the 
other.  For  any  angle  6  =  goc,  we  lay  off  the  distance  ge,  in 
which  the  ratio  of  ge  to  gh  is  the  same  as  the  ratio  of  the  angle  0 
to  360°.  At  the  point  e  determined  in  this  way,  we  erect  a  perpen- 
dicular, ef,  equal  to  ob.  In  this  way  we  can  construct  as  many 
points  as  we  desire.  The  smooth  curve  connecting  these  points 
will  be  a  sine  curve. 

112.  Methods  of  Treating   Alternating-current    Waves. — In 
this"  book,  three   methods  of   representing   alternating-current 
waves  will  be  considered.     Perhaps  the  simplest  and  most  direct 
is  to  use  rectangular  co-ordinates,  giving  a  curve  like  that  shown 
in  Fig.  73.     The  great  advantage  of  this  method  is  that  it  presents 
to  the  eye  a  picture  of  what  is  happening  in  the  circuit.     It  will, 
in  general,  be  employed  in  our  first  consideration  of  a  piece  of 
apparatus.     The  intention  is  that  the  student  should  actually 
see  in  his  own  mind  just  what  must  occur,  before  starting  to  take 
up  the  subject  from  the  mathematical  standpoint. 

113.  Analytical  Method. — The  second  method  of  representing 
the  current  or  e.m.f .  in  an  electrical  circuit,  is  by  means  of  a  mathe- 
matical expression.     Thus,  the  sine  wave  of  Fig.  73  may  be  ex- 
pressed mathematically  as 

i  =  I  sin  ait 

in  which  i  is  the  instantaneous  value  of  the  current,  7  is  the  maxi- 
mum value  which  the  current  attains,  co  is  the  angular  velocity, 
and  t  is  the  time  which  has  elapsed.  It  may  be  further  explained 
that  co  is  the  actual  angular  velocity  of  the  alternator  supplying 
the  current  if  it  is  provided  with  two  poles ;  it  is  twice  the  actual 
angular  velocity,  if  the  machine  has  four  poles,  etc. 

This  method  of  treating  the  subject  has  great  advantages  for 
many  purposes.  It  is,  however,  very  difficult  for  many  students 
to  grasp  the  true  significance  of  the  equations.  In  the  author's 
opinion  it  is  better  suited  to  the  investigation  of  more  advanced 
problems  than  to  the  explanation  of  the  more  simple  relations. 
It  should  also  be  noted  that  the  expressions  for  waves  of  the  non- 
sinusoidal  shape,  become  very  complicated,  and  the  effort  is 
rarely  made  to  work  with  them. 

114.  Vector  Method. — The  third  method  which  we  shall  employ 
is  the  vector  method.     Strictly  speaking,  an  alternating  current 
can  not  be  represented  by  means  of  a  vector,  as  a  vector  has  mag- 
nitude, direction  and  sense.     An  alternating  current  has  no  direc- 


122      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

tion,  considered  over  a  period  of  time.  Even  considered  at  an 
instant,  it  has  only  one  of  two  directions,  and  that  only  at  a 
particular  point  of  the  circuit. 

Referring  to  Fig.  73,  we  have  shown  how  the  sine  curve  may  be 
laid  off  by  means  of  the  circle  with  a  point  rotating  uniformly 
around  it.  A  sine  wave,  if  present  alone  in  a  circuit,  and  if  we 
are  not  interested  in  its  instantaneous  value,  may  be  completely 
defined  by  one  property  alone,  namely,  its  maximum  value.  Thus 
in  Fig.  73  the  radius  or  vector  oc  may  be  considered  as  respresent- 
ing  the  sine  wave  gfih.  We  may  also  think  of  the  vector  oc  as 
rotating  in  a  counter-clockwise  direction,  and,  we  may  consider 
the  instantaneous  value  of  the  current  or  e.m.f.  represented 
by  the  vector  oc  as  being  the  projection  of  this  vector  upon  the 
vertical  line  od.  The  value  of  this  projection  will  obviously  be 


FIG.  74. 

the  same  as  the  value  of  the  ordinate  of  the  sine  wave  ef,  in  fact 
the  sine  curve  was  constructed  by  plotting  these  projections  as 
ordinates  with  the  times  or  the  angles  as  abscissae. 

115.  Phase  Difference. — Usually,  we  have  in  a  circuit  at  least 
two  waves  to  consider.     These  may  be  two  waves  of  current  or 
e.m.f.,  or  a  wave  of  current  and  one  of  e.m.f.     Thus  in  Fig.  74 
we  have  two  alternators  connected  in  series.     The  two  machines 
are  supposed  to  be  mounted  on  the  same  shaft,  and  are  in  such 
an  angular  relation  that  the  e.m.fs.  of  the  two  do  not  reach  their 
maximum  values  at  the  same  time.     The  two  curves  would  be 
drawn  as  shown,  in  Fig.  75.     They  could  be  considered  as  being 
constructed  by  taking  the  projections  of  the  two  points  B  and 
C  on  the  perpendicular  line  ad  in  the  manner  previously  described. 

116.  Addition  of  Two  Waves. — To  get  the  total  or  the  com- 
bined e.m.f.  wave  of  the  two  machines  from  their  individual  waves 


ALTERNATING  CURRENTS 


123 


we  should  proceed  at  any  given  instant  exactly  as  though  we  were 
dealing  with  a  direct-current  circuit.  Thus,  at  the  time  corre- 
sponding to  the  point  a  we  should  take  the  instantaneous  e.m.f., 
ab,  of  the  machine  X  and  add  it  to  ac,  the  e.m.f.  of  the  machine 
F,  giving  as  the  combined  e.m.f.  the  value  ad.  The  same  would 
be  done  with  other  points,  and  the  smooth  curve  as  shown  by 
the  dotted  line  drawn  through  these  points  will  be  the  curve  of 
the  combined  machines.  This  method  could  be  applied  no  matter 
what  the  shapes  of  the  two  waves.  It  would  not  even  be  neces- 
sary that  they  be  of  the  same  shape,  or  frequency. 


FIG.  75. 

117.  Vector  Addition. — If,  however,  we  are  dealing  with  sine 
waves  as  in  the  case  shown,  we  may  arrive  at  the  same  solution  in 
a  simpler  manner  by  using  vectors.  This  is  done  by  drawing  the 
lines  CD  and  BD  parallel  respectively  to  the  lines  AB  and  AC. 
The  resultant  AD  will  represent  the  resultant  wave  in  both  magni- 
tude and  phase.  This  will  be  readily  apparent  if  we  consider  that 
at  any  instant  the  projection  of  the  vector  AD  on  the  line  AE 
is  equal  to  the  sum  of  the  projections  of  the  two  lines  AB  and  AC. 
Thus  Ad'  is  the  sum  of  Ab'  and  b'd'.  Ab'  is  the  projection  of  AB 
and  b'd'  is  equal  to  Ac',  the  projection  of  AC.  Hence,  at  any 
time,  the  projection  of  the  vector  AD  will  be  equal  to  the  sum  of 
the  projections  of  the  two  vectors  AC  and  AB  and  will  represent 
their  combined  value.  This  gives  us  a  very  simple  method  of 
dealing  with  problems  in  alternating  currents.  It  must,  how- 
ever, be  kept  clearly  in  mind  that  solutions  obtained  in  this 
manner  apply  only  to  sine  waves  of  current  and  e.m.f.  Confusion 
is  frequently  caused  by  losing  sight  of  this  fact.  Certain  con- 
ditions frequently  arise  in  circuits  which  tend  to  produce  greatly 


124      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

distorted  waves.  In  this  case,  vector  solutions  have  little  or  no 
value. 

The  addition  of  two  or  more  currents  would  be  carried  out  in 
exactly  the  same  manner.  Thus  if  the  two  alternators  of  Fig. 
74  were  connected  in  parallel,  the  combined  current  would  in 
general  not  be  equal  to  the  arithmetical  sum  of  the  two,  but  to 
their  vector  sum.  The  latter  would  be  obtained  in  the  manner 
just  described,  taking  AB  and  AC  as  currents  instead  of  e.m.fs. 
Frequently  we  are  concerned  only  with  the  relative  values  and 
phase  angles  of  the  different  currents  and  e.m.fs.  In  this  case, 
the  vector  diagram  is  drawn  with  different  angles  between  the 
quantities,  different  e.m.fs.,  etc.,  and  the  changes  can  be  studied 
in  a  general  way.  Sometimes  numerical  values  of  the  results  are 
required.  We  may  obtain  the  result  by  scaling  the  values  directly 
from  the  diagram.  The  accuracy  of  this  method  will,  of  course, 
depend  upon  the  scale  of  the  drawing  and  the  care  with  which  it 
is  made.  It  will,  in  most  cases,  give  results  of  sufficient 
accuracy  for  practical  work. 

If  more  accurate  results  are  required,  they  can  always  be  ob- 
tained by  constructing  the  vector  diagram  and  computing  the 
ength  of  the  lines  representing  the  required  quantities  by  the 
ordinary  rules  of  trigonometry. 

118.  Effective  Values  of  Current  and  E.M.F. — As  we  have  seen, 
an  alternating  current  or  e.m.f.  passes  through  a  series  of  values 
ranging  from  zero  to  a  certain  maximum  in  both  the  positive  and 
negative  directions.  It  is  necessary  in  speaking  of  the  value  of 
a. current  or  an  e.m.f.  to  determine  just  what  is  meant  by  its 
"value."  This  is  defined  by  agreeing  that  a  continuous  cur- 
rent and  an  alternating  current  will  be  considered  the  same  in 
value  if  their  heating  effects  are  the  same  when  passed  through 
the  same  resistance,  i.e.,  if  the  power  lost  is  the  same. 

The  heating  effect  of  a  continuous  current,  or  of  an  alternating 
current  at  any  given  instant,  is  proportional  to  the  square  of  the 
current  at  that  instant.  If  we  have  a  current,  of  whatever 
nature,  which  has  a  varying  value,  its  average  heating  effect  will  be 
proportional  to  its  average  square.  It  is  evident,  therefore, 
that  if  we  are  to  consider  the  power  expended  in  heating  the 
circuit  as  proportional  to  the  square  of  the  value  of  the  current, 
that  we  shall  have  to  consider  this  " value"  as  being  the  square 
root  of  the  average  square.  This  value  is  variously  referred  to 
as  the  effective  value,  the  virtual  value,  the  root  mean  square 


ALTERNATING  CURRENTS  125 

value,  or  the  true  value.  Since  this  is  the  value  usually  of 
interest,  it  is  also  commonly  referred  to  simply  as  the  value  of 
the  current.  If  we  wish  to  consider  the  current  at  the  highest 
point  of  the  wave,  we  refer  to  this  as  the  maximum  value.  Also, 
since  in  a  circuit  of  constant  resistance  the  power  is  equal  to  E2/R, 
the  above  remarks  apply  equally  well  to  the  e.m.f. 

We  can  readily  derive  the  relation  between  the  maximum  value 
of  a  sine  wave  and  the  square  root  of  the  average  square. 
Elementary  trigonometry  gives  the  relation 

sin2  0  +  cos2  0  =  1 

If  we  consider  that  we  pass  through  a  complete  cycle,  the  sine 
will  pass  through  all  values  from  + 1  to  —  1.  The  cosine  will  pass 
through  exactly  the  same  values  as  the  sine.  Then 

average    sin2  0  =  average    cos2  6  =  „ 

and  therefore 

Vaverage   sin2  =  VM  =  0.707 

If  the  maximum  value  of  a  sinusoidal  wave  of  current  or 
e.m.f.  is,  say,  100,  the  effective  value  will  be  70.7.  If  the  effect- 
ive value  is  100,  the  maximum  value  will  be  100  X  \/2  =  141.4. 


PROBLEMS 

47.  An  alternator   having   forty  poles  is  revolving  at  the  rate  of    120 
r.p.m.     What  is  the  frequency?     In  the  case  of  an  alternator  having  ten 
field  poles,  at  what  speed  must  the  machine  revolve  in  order  that  the  fre- 
quency may  be  60  cycles? 

48.  A  circuit  is  carrying  a  60-cycle  alternating  sinusoidal  current  whose 
maximum  value  is  10  amp.     What  is  the  value  of  the  angular  velocity? 
Write  the  equation  of  the  current.     Compute  several  values  of  the  current 
at  intervals  of  0.001  sec.,  starting  from  the  zero  value  of  the  current. 

49.  Represent  the  current  in  the  foregoing  circuit  by  means  of  a  vector. 
Do  the  same  using  rectangular  coordinates,  and  plotting  the  values  obtained 
in  the  above  example. 

60.  Two  alternating  currents  whose  maximum  values  are  100  and  150 
amp.  respectively  differ  in  phase  by  30°.  What  is  the  maximum  value  of 
the  sum  of  the  two  currents?  What  is  the  effective  value? 

51.  Two  e.m.fs.  differ  in  phase  by  90°.     The  sum  of  the  two  is  100  volts 
and  one  of  them  is  75  volts.     What  is  the  other? 

52.  If  there  are  three  sinusoidal  e.m.fs.  of  110  volts  (effective)  each  and 
differing  in  phase  by  120°,  what  two  values  can  be  obtained  for  the  sum  of 
the  three?     What  will  be  the  maximum  values? 


CHAPTER  XII 
INDUCTANCE  AND  CAPACITANCE 

119.  Alternating-  and  Direct-currents  Compared. — In  the  con- 
tinuous-current circuit  we  always  have  the  simple  relation  /  = 
E/R.     A  very  few  experiments  with  alternating  currents  will 
disclose  the  fact  that  in  many  cases  the  current  is  far  from 
the  value  indicated  by  this  equation.     This  variation  may  be 
due  to  the  presence  of  one  or  both  of  two  factors,  inductance 
or  capacitance. 

A  further  investigation  into  the  action  of  alternating  current 
will  show  the  interesting  fact  that  if  we  consider  the  circuit  at  any 
given  instant,  the  current  will  be  given  by  the  same  expression  as 
in  the  case  of  the  direct  current,  namely,  i  =  e/R,  in  which  the 
small  letters  are  used  to  indicate  instantaneous  values.  The 
e.m.f.  e  will,  however,  in  general,  not  be  the  voltage  supplied  by 
the  generator  or  other  source  of  power,  but  will  be  the  algebraic 
sum  of  the  values  of  perhaps  several  e.m.fs.  present  in  the  circuit. 
These  additional  e.m.fs.  may  be  due  to  the  action  of  inductance 
or  of  capacitance.  We  shall  now  proceed  to  consider  how  these 
additional  e.m.fs.  are  generated  and  their  effect  upon  the  circuit 
as  a  whole. 

120.  E.M.F.   Due  to  ^Inductance.— As   previously   noted,  an 
e.m.f.  is  generated  whenever  a  conductor  cuts  lines  of  magnetic 
induction.     The  value  of  this  e.m.f.  is  equal  to  the  number  of 
lines  of  induction  cut  per  second  if  the  cutting  is  uniform,  or  if 
it  is  not  uniform,  the  number  that  would  be  cut  if  the  cutting 
were  to  remain  the  same  for  the  whole  second.     The  number  of 
lines  which  would  be  cut  in  a  second  is  called  the  rate  of  change 
of  the  lines .     This  is  represented  mathematically  by  the  expression 

1     d<p 
=  W~ti 

The  factor  108  is  introduced  to  change  the  unit  of  pressure  from 
absolute  units  to  volts.  If  there  are  several  turns  in  series  in  the 
circuit,  the  e.m.f.  generated  is  increased  in  proportion  to  trie 
number  of  turns,  giving  the  expression 

N    d<? 

=  To8  "5" 

126 


INDUCTANCE  AND  CAPACITANCE 


127 


As  far  as  the  final  result  is  concerned,  it  makes  no  difference 
how  the  lines  of  induction  are  produced.  Figure  76  shows  a 
coil  of  wire  or  solenoid.  Such  a  piece  of  apparatus  is  also  called 
an  inductor.  If  we  thrust  a  permanent  magnet  into  such  a 
solenoid,  we  shall  induce  in  the  coil  an  e.m.f.,  and  if  the  circuit  is 
closed,  a  current.  We  might  equally  well  have  induced  the 
e.m.f.  by  thrusting  the  coil  over  the  magnet,  or  instead  of  the 
permanent  magnet,  an  electromagnet  might  have  been  used. 
Moreover,  in  the  latter  case,  instead  of  thrusting  the  electro- 
magnet into  the  coil  or  the  coil  over  the  electromagnet,  the  same 
result  might  have  been  secured  without  any  movement  of  the 
coil  or  magnet  merely  by  opening  or  closing  the  circuit  through 
the  electromagnet.  This  arrangement  would  constitute  a  simple 
form  of  induction  coil. 


FIG.  76. 

Still  another  form  of  induction  is  possible.  If  we  pass  current 
through  the  coil  of  Fig.  76  we  shall  set  up  in  the  interior  of  the 
solenoid,  lines  of  magnetic  induction.  These  lines,  of  course, 
return  outside  of  the  solenoid,  thus  completing  the  magnetic 
circuit.  It  is  evident  that  while  these  lines  are  being  established 
or  while  they  are  dying  down,  they  will  cut  the  wires  of  the 
solenoid,  thus  inducing  an  e.m.f.  This  e.m.f.  is  represented  by 
the  same  expression  as  before. 

121.  Coefficient  of  Inductance. — It  is,  in  general,  inconvenient 
to  make  computations  with  lines  of  induction.  This  arises 
primarily  from  the  fact  that  magnetic  measurements  are  difficult 
to  make.  It  is  therefore  preferable  to  reduce  our  formulae  to 
forms  involving  current  instead  of  induction. 

In  such  a  coil  of  N  turns  as  that  of  Fig.  76,  the  total  magnetic 
induction,  provided  there  is  no  iron  present,  is  proportional  to  the 
current  times  the  number  of  turns,  or  $  =  KNI'}  or  using  instan- 
taneous values,  <p  =  KNi  where  "K"  is  some  constant.  If  iron  is 


128      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

present,  this  expression  will  still  be  approximately  true,  provided 
that  the  circuit  is  not  saturated.  Substituting  this  value  of  <p  in 
the  equation  we  get 

N    d<p        AT    d(KNi)  _  KN*  di  _       di 
GL  ~  108    dt   :=  108       dt  108    dt  ~       dt 

KN2 

where  L  =  -TT^T  is  called  the  coefficient  of  self-inductance  (or 
108     - 

the  inductance)  of  the  solenoid.  The  unit  of  inductance  is  the 
henry.  This  value  will  be  a  true  constant  if  the  circuit  contains 
no  iron,  but  if  iron  is  present  it  will  in  general,  become  somewhat 
smaller  as  the  current  increases.  Even  in  this  case  it  is  usually 
regarded  as  a  constant  in  theoretical  investigations,  an  average 
value  being  taken. 

122.  Mechanical  Analogy.  —  There  is  a  very  striking  analogy 
between  the  coefficient  of  self  -inductance  of  a  circuit,  and  the 
mass  of  a  body.  As  was  just  pointed  out  the  e.m.f.  required  to 
change  the  current  in  a  circuit  may  be  expressed  as 

di 


In  mechanics,  we  have  an  exactly  analogous  equation.  The 
force  required  to  change  the  velocity  of  a  body,  is  equal  to  the 
mass  of  the  body  times  the  acceleration.  The  acceleration  is 
the  rate  of  change  of  the  velocity,  and  we  may  write, 


Here  we  have  an  exact  analogy  if  for  e.m.f.,  we  substitute  force; 
for  velocity,  current;  and  for  inductance,  mass. 

This  analogy  is  of  help  in  giving  an  accurate  mental  picture 
of  the  actions  taking  place.  It  is  much  easier  to  understand  a 
tangible  phenomenon  than  an  abstract  one. 

Continuing  the  mechanical  analogy  we  may  consider  the  re- 
lation of  friction  and  resistance,  or  electrical  friction.  In  an 
electric  circuit,  we  have 

7  =-f-or#  =  RI 

This  equation  is  exact.  We  may  write  a  similar  equation  for  a 
body  in  uniform  motion 

V  =  -     or  F  =  RV 


INDUCTANCE  AND  CAPACITANCE  129 

where  R  is  the  resistance  to  motion  or  the  friction.  This  equa- 
tion however  is  not  exact,  but  only  an  approximation.  It  illustrates 
excellently  the  fact  already  mentioned,  that  mechanical  engineer- 
ing problems  are  essentially  more  difficult  than  the  correspond- 
ing electrical  ones.  Thus  in  one  class  of  friction,  that  of  bear- 
ings, it  is  generally  stated  that  the  force  due  to  friction  is  con- 
stant, and  does  not  increase  at  all  with  the  velocity.  A  more 
careful  investigation  however  shows  many  irregularities  in  the 
friction  as  the  speed  increases. 

In  another  class  of  friction,  that  of  a  boat  through  the  water, 
the  statement  is  usually  made  that  the  friction  is  proportional  to 
the  square  of  the  speed.  It  is,  however,  a  common  experience 
with  boats  of  a  certain  form,  that  the  friction  at  a  certain  critical 
speed  will  increase  to  a  value  far  above  that  indicated  by  the 
formula.  It  is  almost  impossible  to  drive  such  vessels  beyond  a 
certain  speed.  With  other  hulls  well  adapted  to  high  speeds, 
exactly  the  reverse  is  the  case.  Again  we  have  a  very  complex 
phenomenon,  contrasted  with  the  simple  electrical  one. 

In  the  consideration  of  many  simple  mechanical  problems  as 
for  example,  a  railway  car  at  ordinary  speeds,  or  the  motion  of  a 
fluid  in  a  pipe,  we  shall  be  near  enough  for  our  purposes  if  we 
assume  that  the  formula  given  is  correct,  or  the  force  due  to 
friction  is  proportional  to  the  speed. 

123.  Starting  a  Mass  or  a  Current. — With  these  assumptions, 
the  problems  illustrated  in  Figs.  77  and  78  can  be  solved  by 
identical  mathematical  expressions.  If  we  apply  a  steady  force 
to  a  car  at  rest  as  shown  in  Fig.  78  it  will  gradually  increase  its 
speed  until  a  velocity  is  reached  such  that  the  force  due  to  resist- 
ance is  equal  to  the  propelling  force.  It  will  then  continue  to 
move  at  this  speed,  as  long  as  the  driving  force  is  continued. 
During  the  period  of  acceleration,  the  velocities  at  different  times 
will  be  represented  by  some  such  curve  as  that  shown  in  Fig.  79. 
The  equation  of  this  curve  could  readily  be  determined  by  the 
use  of  differential  equations.  For  the  present  purpose,  it  is  un- 
necessary to  do  so. 

The  electric  circuit  presents  an  exact  analogy  to  this.  A  current 
increases  gradually  instead  of  jumping  at  once  to  its  final  value, 
and  follows  the  same  time  curve  as  in  the  case  of  the  car.  It  is 
true,  however,  that  this  increase  in  current  generally  takes 
place  so  suddenly  that  it  can  not  be  observed  unless  special  in- 
struments are  used.  In  some  instances,  however,  as  for  example, 


130      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

when  a  constant  voltage  is  applied  to  the  field  magnet  of  a  large 
machine  the  change  in  current  can  be  observed  with  consider- 
able accuracy  on  an  ordinary  ammeter.  It  may  be  perhaps  15 


llKXJUUU^'vwvwv) 


4HHW — ' 

B 


.  77. 


Time 

FIG.  79. 


FIG.  78. 


S 


/      Curve  of  Current 
/  Curve  of  E.M.F. 

\ 
Time  \ 


FIG.  80. 

sec.  before  the  needle  of  the  ammeter  ceases  to  move   across 
the  scale. 

The  analogy  can  be  carried  still  further.     If  an  attempt  is  made 
to  stop  the  car  suddenly,  everyone  is  familiar  with  the  result. 


INDUCTANCE  AND  CAPACITANCE  131 

A  very  great  force  is  developed,  and  this  force  is  inversely  pro- 
portional to  the  time  required  to  stop  the  car.  This  force  may 
be  many  times  as  great  as  the  force  applied  to  accelerate  the  car. 
These  facts  are  represented  in  Fig.  80  where  the  velocity  is 
shown  as  a  dashed  line.  This  line  starts  to  descend  rapidly  at 
the  point  A,  indicating  that  the  motion  is  completely  stopped  in 
the  time  BC.  During  the  period  of  acceleration,  a  force  is  ap- 
plied from  outside  in  the  direction  of  the  velocity.  The  car 
pushes  backward  with  the  same  force  as  the  applied  force. 
The  curve  of  back  force  is  shown  by  the  line  DEt  the  force  having 
the  constant  value  OD.  As  soon,  however,  as  an  attempt  is 
made  to  stop  the  body,  it  exerts  force  in  the  direction  in  which 
it  is  moving,  and  continues  to  exert  this  force  as  long  as  the 
retarding  force  is  applied.  The  force  during  this  interval  is 
shown  by  the  curve  E  B  F  C,  and  as  shown,  may  rise  to  a  far 
greater  height  than  the  applied  force,  but  for  a  proportionally 
shorter  time. 

In  the  electric  circuit,  there  will  be  a  similar  action.  Dur- 
ing the  time  that  the  current  is  rising  in  the  coil,  there  will  be 
exerted  a  back  e.m.f.  equal  to  the  applied  voltage.  This  back 
e.m.f.  is  due  partly  to  the  drop  in  the  wire  due  to  resistance, 
and  partly  to  the  tendency  of  such  an  inductive  circuit  to  resist  any 
change  in  the  current.  At  the  instant  of  break,  this  tendency 
exerts  itself  powerfully,  that  is,  the  current  tends  to  continue 
flowing  at  the  same  value,  and  when  forced  to  decrease  by  the 
opening  of  the  circuit,  sets  up  a  large  e.m.f.  The  result  is  a 
heavy  spark  across  the  break,  since  the  induced  e.m.f.  is  sufficient 
to  force  the  current  to  flow  for  a  short  time  across  the  gap  through 
the  air. 

The  amount  of  work  stored  in  such  a  solenoid  (due  to  building 
up  the  magnetic  field)  can  be  readily  obtained.  The  work  done 
during  an  interval  dt  is 

dW  =  eidt 
and  since 

Tdi 

e=Ldt 
we  have 

dW  =  Lidi 

Integrating  this  with  the  limits  i  —  O  and  i  =  I  we  obtain 
W  =  L\ idi  =  ULI2 


=  L\idi  = 
Jo 


132      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

In  a  similar  manner,  we  could  have  derived  an  expression  for  the 
work  stored  in  a  moving  body  of  mass  M  and  would  have  ob- 
tained the  corresponding  expression 

W  = 


The  phenomenon  just  considered  is  made  use  of  in  various 
mechanical  appliances,  such  as  the  hydraulic  ram  and  the  pile 
driver.  In  the  latter,  the  moderate  force  of  gravity  is  increased 
to  the  tremendous  force  of  the  blow  struck  by  the  descending 
weight.  There  is  a  great  increase  of  force,  but  it  must  be  clearly 
noted  that  there  is  no  increase  of  energy.  Though  the  force  of 
the  blow  is  so  great,  it  lasts  such  a  short  time  that  the  actual  work 
(i.e.,  energy)  expended  in  forcing  the  pile  down  is  less  than  the 
work  done  in  raising  the  weight. 

The  corresponding  electrical  device,  the  solenoid  combined 
with  a  battery  and  switch,  is  used  principally  in  one  form  of  gas- 
engine  ignition.  The  switch  is  located  inside  the  cylinder  of  the 
engine  and  the  points  of  the  switch  are  caused  to  separate  at  the 
instant  when  it  is  desired  to  ignite  the  gas.  A  heavy  spark  is 
formed  as  the  points  separate,  and  sufficient  heat  is  produced  to 
ignite  the  mixture. 

124.  Field  Discharge  Switch.  —  If  the  switch  in  the  field  circuit 
of  a  dynamo  or  motor  be  opened  while  current  is  flowing  in  the 
field,  a  heavy  arc  will  be  observed.  The  size  of  this  arc  will  de- 
pend upon  the  amount  of  energy  stored  in  the  field.  In  the  case 
of  a  large  machine  this  may  be  considerable,  and  the  arc  at  the 
time  of  opening  may  be  very  destructive  to  the  switch.  More- 
over, as  just  explained,  there  will  be  a  great  rise  in  voltage  across 
the  terminals  of  the  switch.  It  may  readily  occur  that  with  the 
field  excited  with  current  at  125  volts,  the  voltage  when  the 
switch  is  opened  may  rise  to  1000  volts  or  more. 

This  high  voltage  is  liable  to  puncture  the  insulation  of  the 
fields.  This  danger  can  be  avoided  by  providing  a  side  track,  as 
it  were,  for  the  current.  The  connections  for  this  are  shown  in 
Fig.  81.  When  the  field  is  connected  to  the  line,  the  resistor 
shown  is  not  in  circuit.  As  the  switch  is  opened  to  disconnect 
the  field  from  the  line,  the  resistor  is  first  connected  across  the 
terminals  of  the  field,  and  a  further  movement  of  the  switch 
disconnects  both  from  the  line.  As  soon  as  the  connection  to  the 
line  is  broken,  the  current  begins  to  decrease.  It  is,  however, 
not  forced  to  decrease  to  zero  at  once,  but  is  allowed  to  flow 


INDUCTANCE  AND  CAPACITANCE 


133 


through  the  circuit  of  the  resistor  until  its  energy  is  dissipated. 
Such  a  device  is  known  as  a  field  discharge  switch. 

125.  Resistance  and  Inductance. — We  must  now  examine  the 
effect  of  resistance  and  inductance  in  alternating-current  circuits, 
leaving  the  consideration  of  capacitance  until  later.  In  taking 
up  this  problem  use  will  be  made  of  a  mechanical  analogy  as  in 
the  preceding  case.  The  comparison  is  exact,  with  the  slight 


Field 


FIG.  82. 


exception  of  the  friction  effect,  and  a  complete  understanding  of 
the  one  case  will  give  a  clear  conception  of  the  other. 

126.  Mechanical  Analogy. — Consider  the  electric  circuit  (com- 
prising resistance  and  inductance)  shown  in  Fig.  82.  The 
inductance  corresponds  to  the  mass  of  a  ponderable  body,  while 
the  resistance  corresponds  to  the  friction.  We  could,  therefore, 


FIG.  83. 

devise  many  mechanical  analogies  to  this  circuit.  For  instance, 
the  car  considered  in  the  previous  problem  if  moved  rapidly  back 
and  forth  on  a  level  track  would  afford  an  illustration.  The 
motion  of  the  piston  and  connecting  rod  of  a  steam  or  gas  en- 
gine is  another  familiar  example.  The  motion,  however,  is  not 
sinusoidal  in  this  case,  but  becomes  approximately  so  if  the  con- 
necting rod  is  long  relative  to  the  stroke.  The  deductions  which 


134      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

will  be  arrived  at  presently  can  be  applied  to  this  case  with  the 
foregoing  qualification. 

For  the  present  purpose,  the  hydraulic  analogy  shown  in  Fig. 
83  may  be  considered.  A  piston,  as  shown,  is  supposed  to  be 
moved  back  and  forth  in  a  cylinder.  The  two  ends  of  the  cylin- 
der are  connected  by  means  of  a  pipe.  The  piston  derives  its 
motion  from  a  flywheel  by  means  of  a  Scotch  yoke.  If  the 
rotation  of  the  flywheel  is  uniform,  the  piston  and  the  contents 
of  the  cylinder  and  tube,  if  incompressible,  will  execute  simple 
harmonic  motion.  We  can  then  plot  a  curve  like  the  one  marked 
velocity  or  current  in  Fig.  84,  in  which  the  ordinates  represent  the 
velocity  of  the  piston  at  the  time  represented  by  any  abscissae. 
The  point  A  on  the  curve  corresponds  to  the  end  A  of  the 
cylinder.  Obviously,  at  this  time,  the  velocity  is  zero.  B  repre- 
sents the  point  at  the  middle  of  the  stroke.  The  velocity  is  here 
a  maximum.  At  C,  the  other  end  of  the  stroke,  the  velocity  is 
again  zero.  As  the  piston  starts  to  move  back,  the  velocity  is  in 
the  opposite  direction,  and  the  return  motion  is  indicated  in  the 
figure  by  the  portion  CFE  of  the  curve.  Starting  from  E  the 
cycle  is  again  repeated. 

127.  Resistance  without  Inductance  or  Capacitance. — The 
"force  required  to  cause  the  movement  described  may  be  consid- 
ered under  various  conditions.  First,  let  us  assume  that  the  liquid 
used  in  the  tube  is  so  light  or  that  the  movement  is  so  slow  that 
the  inertia  of  the  liquid  may  be  neglected  in  comparison  with 
the  friction.  For  example,  we  might  use  molasses  for  the  liquid, 
make  the  connecting  tube  small  and  the  motion  slow.  Under 
these  circumstances,  the  inertia  could  evidently  be  neglected 
without  material  error.  This  case  corresponds  to  an  electric 
circuit  with  resistance  but  with  no  inductance.  A  bank  of  incan- 
descent lamps,  or  a  water  rheostat,  would  approximate  this 
condition. 

In  the  case  assumed,  the  only  force  acting  is  that  due  to  fric- 
tion. As  we  have  shown/  we  may  assume  that  the  relation  be- 
tween the  force  and  the  velocity  is  expressed  by  the  equation 

A  =  vR 
or  in  electrical  units 

eR  =  iR 

Since  the  velocity  of  the  liquid  is  expressed  by  an  equation  such  as 

v  =  V  sin  co/ 


INDUCTANCE  AND  CAPACITANCE  135 

or  in  the  electric  circuit 

i  =  /  sin  ut 

it  is  evident  that  the  expressions  for  the  force  will  be  respectively 
/R  =  R  V  sin  ut,  and  eK  =  RI  sin  ut 

We  can  therefore  draw  the  force  curves  in  either  case  as  shown 
in  Fig.  84.  The  force  will  be  zero  at  the  same  time  that  the 
velocity  or  the  current  is  zero,  and  will  be  a  maximum  when  the 
above  quantities  are  a  maximum.  In  a  case  like  this,  we  say 
that  the  current  and  the  e.m.f.  (or  the  velocity  and  the  force)  are 


The  power  involved  in  the  foregoing  action  is  of  great  interest. 
Power  is  the  product  of  force  and  velocity,  or  in  electrical  units, 
of  current  and  e.m.f.  Even  though  the  force  and  velocity  or 
the  current  and  e.m.f.  are  variable,  this  relation  holds  if  we 
consider  the  power  at  any  instant.  Thus  using  small  letters  to 
indicate  instantaneous  values, 

p  =  vf  or  p  =  ei 

Thus  in  Fig.  84,  if  we  consider  any  time  such  as  that  represented 
by  the  point  G  the  power  at  this  instant  will  be  the  product  of 
the  current  or  velocity,  GI,  times  the  force  or  e.m.f.,  GJ,  giving 
some  such  value  as  GH.  The  maximum  value  of  this  product 
will  evidently  be  at  the  time  when  the  current  and  e.m.f.  (or  the 
velocity  and  the  force)  are  a  maximum.  The  power  will  also  be 
zero  whenever  either  one  of  the  two  factors  is  zero.  The  power 
will  never  be  negative,  since  when  one  of  the  factors  becomes 
negative,  the  other  is  negative  also  and  the  product  of  two  nega- 
tive quantities  is  positive.  This  will  also  be  evident  if  we  con- 
sider that  at  the  flywheel  rim  the  torque  or  turning  moment  will 
at  all  times  have  to  be  in  the  same  direction,  though  it  will  drop 
to  zero  just  at  the  instant  when  the  piston  is  at  the  end  of  its 
stroke.  We  have  then  a  condition  in  which  the  power  is  pulsat- 
ing but  always  positive;  that  is,  the  mechanism  or  the  electric 
generator  always  requires  power  to  drive  it  except  at  an  instant 
at  the  zero  points,  and  never  acts  to  return  power  to  the  flywheel 
in  the  one  case,  nor  to  the  driving  engine  in  the  other. 

128.  Inductance  without  Resistance. — If,  on  the  other  hand, 
We  consider  that  the  cylinder  and  connecting  tube  in  Fig.  83  are 
filled  with  some  heavy  liquid  like  mercury,  that  the  passage  is 


136      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

short  and  large  in  section,  and  that  the  movement  of  the  piston 
is  rapid,  the  conditions  will  be  entirely  changed.  In  this  case,  we 
may  consider  that  the  friction  is  so  small  in  comparison  with  the 
inertia,  that  it  may  be  neglected.  A  moment's  consideration  will 
show  that  the  force  required  to  overcome  the  inertia  of  the  piston 
will  be  greatest  when  the  piston  is  at  rest.  To  keep  it  in  motion 
at  a  uniform  speed,  will  require  no  force  at  all,  under  the  assump- 
tion we  have  made,  that  the  friction  is  zero.  At  the  time  A  (see 
Fig.  85)  we  shall  have  to  exert  the  maximum  force  to  start  the 
mass  into  motion.  The  required  force  will  become  less  as  the  ve- 
locity increases,  and  will  be  zero  when  the  piston  is  at  the  center  of 
its  stroke.  This  corresponds  to  the  point  B.  Beyond  this  point, 
instead  of  a  push  on  the  piston,  a  pull  will  be  required  to  bring 
the  moving  mass  to  rest.  This  we  represent  as  a  negative  force, 
and  the  curve  of  force  or  e.m.f.  consequently  passes  below  the 
zero  line  at  the  point  B.  If  the  reader  will  imagine  himself  to 
be  pushing  a  heavy  lawn  roller  to  and  fro  on  a  smooth  level  sur- 
face such  as  a  stone  sidewalk,  he  will  readily  understand  the  fore- 
going relations  of  force  and  velocity.  In  this  case,  we  say  the 
current  or  the  velocity  lags  90°  behind  the  e.m.f.  or  the  force. 
That  the  current  is  behind,  will  be  apparent  if  we  consider  that 
as  we  pass  from  left  to  right,  the  e.m.f.  attains  its  maximum  value 
before  the  current. 

129.  Power  in  Inductive  Circuit. — The  curve  of  power  can  be 
constructed  in  the  same  manner  as  before.  It  will  cross  the  zero 
axis  whenever  either  the  current  or  the  e.m.f.  is  zero.  In  the  pres- 
ent case,  it  is  evident  that  one  of  the  factors  is  sometimes  nega- 
tive, while  the  other  is  positive.  Hence  we  shall  have  negative 
values  of  the  power.  In  fact,  if  the  curve  of  power  is  accurately 
constructed,  the  positive  portions  will  be  of  exactly  the  same  area 
as  the  negative  ones,  or  the  net  power  is  zero. 

The  explanation  of  this  apparently  peculiar  fact  is  that  the 
liquid  requires  a  push  to  set  it  in  motion,  but  while  it  is  slowing 
down,  it  on  the  other  hand  exerts  a  push  on  the  piston.  Thus, 
during  the  first  quarter  revolution,  torque  must  be  applied  to  the 
flywheel  in  the  direction  of  rotation.  During  the  next  quarter 
turn,  however,  the  inertia  of  the  liquid  will  tend  to  keep  up  the 
motion  and  will  return  just  as  much  work  as  was  done  upon  it 
during  the  preceding  quarter.  The  apparatus  then  acts  during 
half  the  time  as  a  pump,  and  during  the  other  half  as  an  hydraulic 
motor.  In  the  electric  circuit,  a  similar  action  takes  place,  the 


INDUCTANCE  AND  CAPACITANCE  137 

dynamo  machine  acting  as  a  generator  for  half  the  time  and  as  a 
motor  for  the  remaining  time.  It  is  thus  alternately  retarded  and 
forced  ahead,  and  the  net  power  required  is  zero. 

The  above  applies,  of  course,  only  in  the  assumed  case  of  zero 
friction  or  zero  electrical  resistance.  In  practice,  we  can  not 
have  an  apparatus  without  friction,  or  an  electric  circuit  without 
resistance.  Hence  the  condition  stated  can  not  be  exactly  realized, 
but  a  very  near  approximation  can  be  made  to  it.  The  fact  that 
the  average  power  would  be  zero,  might  have  been  predicted  at 
once,  since  if  there  is  no  friction,  there  would  be  no  opportunity 
to  dissipate  any  power.  Similarly,  in  the  electric  circuit,  if 
there  is  no  resistance  in  the  circuit  shown,  there  is  no  chance  for 
any  loss  of  power,  and  consequently  the  net  power  must  be 
zero. 

130.  Application  to  Steam  Engine. — An  excellent  applica- 
tion of  these  principles  is  afforded  in  the  case  of  the  modern 
high-speed  steam  engine.  It  was  at  first  thought  essential  by 
many  engineers  that  the  reciprocating  parts  of  such  engines 
should  be  made  as  light  as  possible  in  order  to  avoid  vibration. 
This  is  an  incorrect  view  of  the  matter.  By  making  the  piston, 
piston  rod  and  connecting  rod  moderately  heavy,  it  is  possible 
to  bring  these  parts  to  rest  at  the  end  of  the  stroke  by  means  of 
the  compression  of  the  steam,  purposely  trapped  in  the  cylinder 
by  the  closing  of  the  exhaust  valve  slightly  before  the  piston 
reaches  the  dead  center.  At  the  beginning  of  the  succeeding 
power  stroke,  the  heavy  reciprocating  parts  serve  to  take  the 
principal  force  of  the  impulse  of  the  steam,  thus  relieving  the 
crank  pin  from  the  sudden  impulse.  As  the  end  of  the  stroke  is 
reached,  the  force  of  the  steam  becomes  less.  The  motion  of  the 
piston  and  other  parts  is  however  now  being  retarded,  and  they  in 
consequence  exert  pressure  on  the  crank  pin,  in  addition  to  the 
force  of  the  steam.  In  this  manner,  the  turning  moment  of  the 
engine  is  rendered  much  more  uniform  than  would  be  the  case 
if  the  reciprocating  parts  were  light.  It  might  also  be  well  to 
point  out  that  the  foregoing  demonstration  shows  that  aside 
from  the  friction  always  present,  the  power  expended  in  recip- 
rocating a  weight  such  as  that  of  the  piston  of  a  steam  engine 
is  zero.  It  seems  well  to  mention  this  point,  since  many  people 
imagine  that  a  large  amount  of  power  is  wasted  in  this  way  in  the 
reciprocating  steam  engine.  This  belief  has  no  foundation  in 
fact. 


138      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

131.  Circuits  Having  Both  Resistance  and  Inductance. — As 
previously  stated,  it  is  impossible  in  practice  to  have  electric 
circuits   entirely   free   from   resistance,    or   mechanical   circuits 
free  from  friction.     In  practice,  the  condition  which  most  fre- 
quently occurs  in  electrical  circuits,  is  that  shown  in  Fig.  82; 
where  both  resistance  and  inductance  are  present.     To  construct 
the  curves  for  this  circuit,  we  draw  the  current  curve  as  before 
(see  Fig.  86).     It  is  now  evident  that  we  shall  at  any  time  have 
present  two  forces,  one  due  to  the  resistance  of  the  circuit,  the 
other  that  necessary  to  overcome  the  effect  of  the  inductance. 
We  can  plot  these  two  curves  separately  as  shown  by  the  dashed 
curves  in  the  figure.     To  get  the  curve  of  total  applied  e.m.f., 
we  have  only  to  add  the  corresponding  values  of  the  two  compo- 
nent e.m.fs.  at  any  given  point.     The  smooth  line  drawn  through 
these  points  will  be  the  required  curve. 

To  obtain  the  curve  of  power,  we  should  proceed  as  before, 
obtaining  the  various  points  by  multiplying  together  the  corre- 
sponding values  of  the  current  curve  and  the  curve  of  resultant 
e.m.f.  This  procedure  gives  the  curve  marked  "  Power."  It 
will  be  seen  that  the  power  is  partly  positive  and  partly  negative, 
the  positive  portion,  however,  being  much  greater  than  the  nega- 
tive portion.  The  net  power  will  be  obtained  by  subtracting 
the  area  of  the  negative  portions  from  the  area  of  the  positive 
portions. 

132.  Vector   Representation. — We    can    show    the   foregoing 
relations  in  a  simpler  manner  by  means  of  vector  representation. 
Figures  84,  85  and  86  correspond  respectively  to  Figs.  87,  88  and 
89.     In  Fig.  87,  the  fact  that  the  current  and  the  e.m.f.  are  in 
the  same  phase  is  represented  by  drawing  the  vectors  parallel 
to  one  another.     For  the  case  of  a  circuit  containing  inductance 
only  (see  Fig.  88),  the  current  vector  may  first  be  drawn.     The 
vector  representing  the  e.m.f.  will  then  be  drawn  so  as  to  be  90° 
ahead  of  the  current,  or  the  current  90°  behind  the  e.m.f.     In  the 
event  of  both  inductance  and  resistance  being  present,  we  may 
first  draw  the  current  vector  as  shown  in  Fig.  89.     The  e.m.f. 
required  to  overcome  resistance  is  drawn  in  phase  with  the  cur- 
rent; that  consumed  by  the  inductance,  90°  ahead  of  it.     The 
total  applied  e.m.f.  will  be  the  resultant  of  these  two  e.m.fs.  or 
the  line  OE. 

133.  Calculation  of  Power. — To  find  an  expression  for  the 
power  in  Fig.  89  we  may  consider  the  actual  e.m.f.  OE  as  due  to 


INDUCTANCE  AND  CAPACITANCE 


139 


FIG.  84. 


FIG.  85. 


FIG.  86. 


E 


Force  or  E.M.F.- 


f-« Force 

|< Veloci 


7 


ity  or  Current    -H 

FIG.  87. 


Current  or  Velocity 
FlG.   88. 


140      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


two  components  OEL  and  OER.  As  we  have  shown,  the  compo- 
nent OEL  and  the  current  01  would  represent  zero  power,  since 
they  are  at  right  angles.  The  total  power  is  then  the  product 
of  01  and  OER  or 

P  =  01  '  OER 

It  is  evident,  however,  that  OEK  =  OE  cos  0.  Making  this 
substitution, 

P  =  El  cos  0 


:  > 


RI  — >T  * 
FIG.  89. 


or  the  power  in  an  alternating-current  circuit  is  the  product  of 

the  effective  values  of  the  current 
and  the  e.m.f.  times  the  cosine  of 
the  angle  of  lead  or  lag  of  the  cur- 
rent. It  must  be  remembered, 
however,  that  the  expression  angle 
of  lag  or  lead  has  a  definite  mean- 
ing only  in  the  case  of  sine  waves 
of  current  and  e.m.f.  In  the  case 
*J  of  distorted  waves  we  may  assume 
an  angle  which  would  give  the 
same  result.  This  assumed  angle 
has,  however,  no  definite  physical  meaning. 

134.  Mathematical  Treatment. — The  above  facts  can  be 
deduced  in  a  very  simple  manner  by  a  mathematical  treatment. 
It  is,  however,  the  opinion  of  the  author  that  the  physical  inter- 
pretation, presented  in  a  manner  similar  to  that  given  above, 
should  be  thoroughly  understood  before  an  attempt  is  made  to 
study  the  mathematical  treatment. 

Assuming  a  current  represented  by  the  formula, 

i  =  Im  sin  wt 

acting  in  a  circuit  where  the  inductance  is  zero  and  the  resistance 
is  R,  we  shall  at  any  instant  require  an  e.m.f.  equal  to  Ri,  or  the 
expression  for  the  e.m.f.  at  any  instant  will  be 

eR  =  RIm  sin  at 

In  the  case  of  a  circuit  containing  only  inductance,  the  e.m.f. 
at  any  instant  required  to  balance  the  back  e.m.f.  is  given  by  the 
formula, 

di 


INDUCTANCE  AND  CAPACITANCE  141 

Substituting  and  performing  the  differentiation,  we  obtain 
eL  =  L-^dm  sin  co£)  =  L/mco  cos  cot  =  L/wco  sin  (cot  +  90°) 

The  instantaneous  value  of  the  required  e.m.f.  is  equal  to  the 
maximum  current  times  the  coefficient  of  self-induction,  times 
the  angular  velocity,  times  sin  (co£  -f-  90°),  and  is  advanced  in 
phase  by  an  angle  of  90°. 

The  above  e.m.fs.  may  be  represented  by  means  of  vectors. 
The  length  of  the  vector  may  be  either  the  maximum  values  of  the 
quantities  or  the  effective  values,  since  the  two  are  proportional. 
The  latter  are  used  in  the  diagrams.  If  maximum  values  are 
used  the  length  of  the  vector  will  be  L/mco  or  if  effective  values, 
L/co  where  7  =  Im  +  \/2.  The  total  applied  e.m.f.  will  be  the 
vector  sum  of  the  two  e.m.fs.  Since  the  angle  between  the  vec- 
tors is  90°,  this  resultant  will  evidently  be  (see  Fig.  89) 


or  transposing, 


If  E  is  the  effective  value  of  the  e.m.f.,  /  is  the  effective  cur- 
rent. This  is  one  of  the  most  important  equations  in  electrical 
engineering. 

The  value  of  the  angle  6  between  the  resultant  e.m.f.  and  the 
current  is  given  by  the  relation 

Leo 

tan  6  =  -5- 
rC 

If  desired,  we  may  also  find  the  angle  from  the  equations, 

R 

COS  U    —        /  -  .  - 

\/R2  +  L2w2 

or 

Leo 

sin  0  =  — 

L2to2 


135.  Power.  —  The  power  at  any  instant  is  given  by  the  expres- 
sion 

p  =  ei  =  Im  sin  <f>  -  Em  sin  (<f>  +  0) 

in  which  we  have  for  convenience  represented  the  angle  cot  by 
the  letter  </>.     To  obtain  the  average  power  in  the  circuit,  it  is 


142      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

necessary  that  we  integrate  this  expression  through  an  angle 
great  enough  to  comprise  one  or  more  complete  cycles  of  the 
power,  and  divide  the  result  by  the  angle  comprised  in  the  cycle. 
We  then  have,  integrating  through  the  angle  ?r, 


sin  <f)  -  sin  (<f>  +  6)d<j>  = 
w    oj 
E, 


Emlm    i  ""    . 
P  =  -  I     si] 

w.  r*    • 

-    I     (sin2  0  cos  6  +  sin  <f>  •  cos  </>  sin  6)d<f>  = 
T     oj 

Emlm[  (4  1       •        OJLX  -        n       1       •     2      .  ~l*  E  ™I  m 

(~~  —  -T  sin  20)  cos  6  +  sin  6  •  ~  sin2  0        =  —  x—  cos  0 

TT        L  \Z  Z  .1  Q  Zi 

The  current  and  the  e.m.f.  in  the  above  are  the  maximum  values. 
To  substitute  effective  values  for  maximum  values  we  must 
multiply  each  by  \/2.  This  gives  as  the  final  result,  if  E  and  / 
are  effective  values, 

P  =  El  cos  0 

or  the  same  result  that  we  obtained  by  means  of  the  graphic 
method. 

136.  Power  Factor.  —  In  a  circuit  carrying  direct  current  the 
power  is  always  the  product  of  the  volts  and  the  amperes.  In 
an  alternating-current  circuit  the  power  can  never  be  more  than 
this,  but  is  usually  less.  We  define  power  factor  by  the  expres- 
sion, 

.  watts 

power  factor  =  —  rr  —  rz  — 

volts  X  amperes 

or 


El 

From  the  preceding  article  it  will  be  seen  that  in  the  special 
case  of  harmonic  e.m.f.  and  current, 

P 

P.F.   =  777   =   COS  0. 
Mil 

It  will  be  evident  that  the  power  factor  can  never  be  greater 
than  one,  but  it  may  be  anything  from  one  to  zero. 

137.  The  Condenser.  —  A  condenser  consists  of  two  conductors 
separated  by  a  dielectric,  that  is,  by  a  body  which  is  not  a  con- 
ductor of  electricity.  For  example,  two  plates  of  metal  separated 
from  one  another  by  a  layer  of  air  or  a  sheet  of  glass  make  an 
excellent  condenser  for  some  purposes.  If  the  two  plates  of  such 
a  condenser  be  connected  to  the  two  poles  of  a  source  of  elec- 


INDUCTANCE  AND  CAPACITANCE 


143 


tricity  as  shown  in  Fig.  90,  a  momentary  current  will  flow  from 
the  cell  into  the  condenser.  The  current  will  last  only  for  a 
moment,  until  a  certain  quantity  of  electricity  has  passed  into 
the  condenser.  The  condenser  retains  the  electric  charge.  This 
charge  can  produce  a  current  if  we  disconnect  the  terminals  from 
the  battery  and  connect  them  by  means  of  a  conductor.  This 
current,  like  the  charging  current,  will  be  only  momentary. 

An  analogous  hydraulic  circuit  is 
shown  in  Fig.  91.  The  pump  P 
which  is  here  assumed  to  be  a  cen- 
trifugal pump,  operating  at  such  a 
speed  as  to  produce  a  constant  water 
pressure,  corresponds  to  the  battery. 
The  cell  containing  a  flexible  dia- 
phragm corresponds  to  the  condenser. 
When  the  circuit  is  first  completed 
by  connecting  the  diaphragm  cham- 
ber to  the  pump,  a  momentary  cur- 
rent of  water  will  flow.  This  ceases 
almost  at  once,  but  a  permanent 
displacement  of  the  water  remains. 
This  is  analogous  to  the  charge  of 
electricity.  If  the  pump  is  discon- 
nected and  the  water  circuit  com- 
pleted by  means  of  a  pipe,  a  mo- 
mentary current  in  the  reverse  direc- 
tion will  flow  and  the  " charge"  of 
water  will  disappear,  that  is,  the 
diaphragm  will  return  to  its  original  position. 

The  quantity  of  electricity  is  the  product  of  the  current  and 
the  time  during  which  the  flow  continues.  If,  as  in  the  present 
instance,  the  flow  is  variable,  the  quantity  is  the  integrated  value 
of  the  product  of  the  current  and  the  time.  It  has  been  found 
that  the  quantity  is  proportional  to  the  applied  e.m.f.,  and  we  may 
write  the  equation 

Q  =  CE 

in  which  Q  is  the  quantity,  E  is  the  applied  e.m.f.,  and  C  is 
known  as  the  capacitance  (formerly  called  capacity)  of  the  con- 
denser. In  the  case  of  the  hydraulic  circuit  we  may  write  a 
similar  equation 

Q  =  CP 


FIG.  90. 


144      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

in  which  Q  is  the  quantity  of  water  displaced,  C  is  the  "  capaci- 
tance" of  the  flexible  diaphragm,  and  P  is  the  pressure. 

We  may  increase  the  capacitance  of  the  condenser  by  increasing 
the  area  of  the  plates,  by  placing  the  plates  nearer  together,  and 
by  changing  the  dielectric  used.  For  large  capacitance  when 
only  moderate  pressures  are  to  be  used,  the  distance  between  the 
plates  is  made  very  small  and  the  plates  are  of  large  size.  Since 
the  plates  are  near  together,  the  use  of  air  insulation  is  imprac- 
ticable. In  any  event,  other  substances  cause  the  condenser  to 
have  a  greater  capacitance,  and  hence  would  be  preferred.  The 
dimensions  of  the  condenser  would  also  be  too  great  if  only  two 

plates  were  used,  and  hence  it 

is  customary  to  pile  up  a  num- 
ber of  sheets  of  the  conductor, 
separating  adjacent  sheets  by 
the  dielectric  used.  This  lat- 
ter is  usually  mica  or  paraf- 
fined paper. 

The  unit  of  quantity  of  elec- 
tricity is  the  coulomb.     This 
is  the  quantity  of  electricity 
FlG>  91  stored  in  a  condenser  when  1 

amp.  flows  into  it  for  1  sec. 

If  a  condenser  takes  a  charge  of  1  coulomb  when  charged  to 
a  pressure  of  1  volt,  its  capacitance  is  said  to  be  1  farad.  A 
condenser  of  such  a  capacitance  would  be  of  extremely  large  size. 
Consequently,  a  unit  of  one  millionth  of  the  above  value  is 
preferable  for  ordinary  use.  This  is  known  as  the  microfarad. 
A  condenser  of  a  capacitance  of  1  microfarad  and  capable  of 
withstanding  500  volts  would  have  a  volume  of  about  50  cu.  in. 
As  is  evident  from  the  foregoing,  a  steady  current  either  of 
electricity  or  of  water  can  not  long  exist  in  a  circuit  in  which  a 
condenser  is  placed.  In  the  case  of  an  alternating  current  either 
of  electricity  or  of  water,  the  quantity  of  electricity  or  of  water 
conveyed  in  the  one  direction  or  the  other  during  one  wave  will 
in  general  not  be  very  large,  but  the  current  may  be  large.  This 
is  particularly  true  if  the  frequency  is  high.  In  this  case  a  con- 
denser may  offer  but  little  apparent  resistance  to  the  passage  of 
the  current.  In  fact,  as  will  be  shown  presently,  if  the  circuit 
contains  inductance  or,  in  the  case  of  the  hydraulic  analogue,  if 
inertia  is  present,  the  introduction  of  the  condenser  or  diaphragm 
may  actually  increase  the  flow  of  current. 


INDUCTANCE  AND  CAPACITANCE 


145 


138.  Circuit  Containing  a  Condenser  Only. — To  understand 
the  action  more  fully,  consider  the  electric  circuit  of  Fig.  92  or 
the  hydraulic  circuit  of  Fig.  93.  In  the  former  we  have  an 
alternator  supplying  current  to  a  condenser.  In  the  latter  the 
reciprocating  piston  forces  an  alternating  current  of  water 
through  the  pipe.  We  may  imagine  that  the  water  is  without 
mass  or  friction,  so  the  inertia  and  friction  effects  may  be  neg- 
lected. The  diaphragm  is  at  its  central  position  and  is  exerting 
no  pressure  when  the  piston  is  at  its  middle  point.  The  curves 
of  pressure  or  e.m.f.,  quantity,  and  current  for  the  two  cases 
are  shown  in  Fig.  94.  Consider  the  time  when  the  piston  is  at 
the  end  of  the  stroke.  The  diaphragm  will  be  displaced  to  its 
greatest  extent,  and  consequently  the  pressure  on  it  will  be  at 


FIG.  92. 


FIG.  93. 


its  maximum.     This  position  of  the  piston  corresponds  to  the 
point  A  on  the  diagram. 

We  may  assume  as  before  that  the  curve  of  current  is  a  sine 
curve.  The  curve  of  quantity  of  water  or  electricity  displaced 
will  evidently  coincide  with  the  curve  of  displacement  of  the 
piston  and  of  the  pressure.  A  moment's  consideration,  however, 
will  show  that  the  current  will  be  zero  at  the  time  when  the  quan- 
tity displaced  is  a  maximum.  This  is  evident  in  the  case  of  the 
hydraulic  system,  since  at  this  time  the  piston  is  at  the  end  of 
the  stroke  and  the  flow  or  current  must  consequently  be  zero. 
As  the  pressure  begins  to  decrease  beyond  A  the  water  or  elec- 
tricity begins  to  flow  out  of  the  diaphragm  chamber  in  the  one 
case,  or  out  of  the  condenser  in  the  other.  This  flow  will  be 
against  the  direction  of  the  pressure.  Consequently,  we  must 

draw  the  current  curve  sloping  downward  from  the  point  A. 
10 


146      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


At  the  time  when  the  pressure  or  e.m.f.  is  zero  the  flow  will 
evidently  be  greatest,  since  the  piston  is  then  moving  with  its" 
greatest  velocity,  as  it  is  at  the  center  of  its  stroke.  We  can 
continue  in  this  way  to  plot  other  points  of  the  current  curve, 
finally  obtaining  some  such  shape  as  shown.  An  inspection  of 
this  will  show  that  the  current  reached  its  maximum  value 
before  the  pressure.  Moreover,  since  the  displacement  is  90°, 
we  may  conclude  that  in  a  condenser  the  current  leads  the 
applied  e.m.f.  by  an  angle  of  90°.  It  will  be  recalled  that  this 
is  just  the  reverse  of  the  case  of  an  inductance  in  which  the 
current  lags  behind  the  applied  e.m.f.  by  90°. 

We  could  readily  draw  the  curves  of  power  corresponding  to 
the  curves  of  Fig.  94.  From  what  has  gone  before,  it  will  be 
evident  that  the  net  power  will  be  zero.  This  is  so  since  all  of 
the  work  done  in  deflecting  the  diaphragm  of  Fig.  93  will  be 


FIG.  94. 

restored  when  the  diaphragm  assumes  its  normal  position. 
Should  there  be  some  friction  due  to  the  movement  of  the  dia- 
phragm, or  should  it  not  assume  exactly  its  original  position  when 
relieved  from  strain,  some  power  would  be  lost.  There  is  in 
every  condenser  some  loss  analogous  to  this  effect.  When  a 
condenser  is  charged,  there  is  an  actual  strain  on  the  molecules 
of  the  dielectric.  This  causes  a  certain  deformation  and  a  con- 
sequent molecular  friction.  Consequently,  there  is  some  loss 
of  power,  but  in  general  this  is  so  small  that  it  may  be  entirely 
neglected.  This  molecular  friction  in  a  condenser  is  known  as 
dielectric  hysteresis. 

139.  Capacitance  of  Transmission  Lines. — In  general,  con- 
densers are  not  used  to  any  great  extent  in  electrical  engineering 
in  connection  with  power  machinery.  They  do  find  extensive 
use  in  telephone  practice  and  other  applications.  In  power 
machinery,  the  principal  reason  for  studying  their  effects  is  that 


INDUCTANCE  AND  CAPACITANCE  147 

these  effects  can  be  duplicated  by  the  use  of  synchronous  motors 
or  generators.  This  will  be  explained  in  connection  with  these 
machines.  It  is  also  a  fact  that  there  is  present  in  all  long  trans- 
mission lines  a  decided  condenser  effect.  This  is  due  to  the  fact 
that  the  two  or  more  wires  used  in  such  a  transmission  constitute, 
with  the  surrounding  air  as  dielectric,  a  condenser  of  consider- 
able capacitance.  It  is  true  that  the  wires  are  far  apart  which 
tends  to  decrease  the  capacitance,  but  as  the  length  is  often 
more  than  100  miles  the  total  capacitance  is  considerable.  More- 
over, very  high  voltages,  frequently  of  100,000  volts  or  more, 
are  used  on  such  lines.  At  this  pressure,  the  line  current  is 
correspondingly  small  and  therefore  the  charging  current  will  be 
a  very  considerable  fraction  of  the  full-load  line  current.  A  line 
of  200  miles  operating  at  100,000  volts  will,  for  example,  require 
a  current  about  equal  to  the  full-load  current  of  a  2000-k.v.a. 
alternator.  Hence,  on  such  a  line,  it  would  be  impossible  to 
use  units  of  less  than  the  stated  capacity  since,  even  though 
there  were  no  load  on  the  line,  the  machine  would  be  burned  out 
in  trying  to  supply  the  charging  current  to  the  line. 

The  above  effects  are  even  greater  in  cables  adapted  to  be 
placed  underground.  In  this  case  the  conductors,  in  order  to 
keep  the  cable  of  reasonable  size,  are  close  together.  Conse- 
quently, the  capacitance  per  mile  is  large.  Fortunately,  such 
cables  are  usually  of  moderate  length  only,  and  are  rarely  ope- 
rated at  pressures  of  more  than  22,000  volts.  Even  so,  trouble 
is  sometimes  encountered  on  account  of  condenser  effects. 

140.  Circuits  Containing  Resistance,  Inductance  and  Capaci- 
tance.— We  have  now  to  consider  the  more  general  case  of  a 
circuit  containing  resistance,  capacitance  and  inductance.  These 
three  elements  are  found  in  all  commercial  circuits.  It  is  true,  as 
already  pointed  out,  that  the  effect  of  the  capacitance  is  usually 
relatively  unimportant.  In  some  cases,  however,  the  capacitance 
of  the  line  may  be  considerable,  and  even  though  this  is  not  the 
case,  synchronous  machinery  may  be  present  at  the  end  of  the 
line,  and  by  taking  a  leading  current  cause  essentially  the  same 
effects  as  would  be  caused  by  the  presence  of  capacitance. 

An  electric  circuit  of  this  kind  is  shown  in  Fig.  95.  Its 
mechanical  analogue  is  represented  in  Fig.  93,  if  we  assume  that 
the  liquid  used  has  mass  and  also  exerts  friction  upon  the  tubes. 
When  only  resistance  and  inductance  were  present  in  the  circuit, 
we  had  two  forces  to  consider :  that  to  overcome  friction  or  electri- 


148      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

cal  resistance,  and  that  to  overcome  the  self-induced  e.m.f.  or 
the  inertia  of  the  liquid.  To  these  forces  we  have  now  added 
a  third,  the  e.m.f.  required  to  charge  the  condenser,  or  the  force 
necessary  to  distort  the  diaphragm. 

Figure  96  shows  the  curves  corresponding  to  this  case.  As 
before,  we  start  by  drawing  the  curve  of  current.  The  applied 
e.m.f.  required  to  overcome  the  resistance  is  shown  by  a  sine 
wave  in  phase  with  the  current.  The  e.m.f.  required  to  overcome 
the  inductance  is  90°  ahead  of  the  current,  while  that  to  over- 


FIG.  95. 


FIG.  96. 

come  the  capacitance  is  90°  behind  the  current.  The  resultant 
e.m.f.  at  any  instant  is  the  algebraic  sum  of  the  three-component 
e.m.fs.  Thus  at  the  time  corresponding  to  the  dashed  vertical 
line  we  have: 

Electromotive  across  the  resistor  =  -  2.5 
Electromotive  across  the  inductor  =  —  11.3 
Electromotive  across  the  condenser  =  -f  6.1 

Sum  =  instantaneous  value  of  the 
resultant  e.m.f  .s. .  .  =  —    7.7 


INDUCTANCE  AND  CAPACITANCE 


149 


The  above  values  are  scaled  from  the  curves. 

141.  Vector  Representation. — These  relations  are  more  clearly 


Liu 


X^y^-Angle  oJ:  Lead 


pplied  E.M.F. 


_%J 


FIG.  97. 


FIG.  98. 


r 


Liu 


shown  by  the  vector  diagram  of  Fig.  97.  Starting  with  the 
current  as  before,  the  e.m.f.  consumed  by  resistance  is  drawn  in 
phase  with  the  current,  and  those  consumed  by  inductance  and 
capacitance  respectively  90°  ahead 
and  90°  behind  the  current.  The 
resultant  of  the  e.m.fs.  over  the 
reactor  and  over  the  condenser  is 

readily   obtained  by  taking  their  H Ri 

arithmetical  difference.     This  dif-      *  * 

f erence,  combined  vectorially  with  Applied  E.M.F. 

the  e.m.f.  required  by  the  resis- 
tance, gives  the  applied  e.m.f. 
The  angle  of  lag  or  lead  of  the 
current  with  respect  to  the  e.m.f.  FJG  99 

will  be  as  shown.     Figure  98  shows 

a  case  where  the  drop  over  the  condenser  is  greater  than  that 
over  the  inductor,  causing  the  current  to  lead  the  resultant  e.m.f. 
In  Fig.  99  the  capacity  and  inductive  e.m.fs.  are  equal,  and  the 
current  neither  leads  nor  lags. 

142.  Mathematical  Treatment.— We  can  readily  deduce  the 
same  facts  mathematically.     Let 


Cu 


150      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

i  =  Im  sin  co£ 
then  the  maximum  e.m.f.  across  the  condenser  will  be 

m 

EMC  =  Q/C  =  "-f-  -  .»  £  cos  ut 

O  CO 

or  using  effective  values 


•"v       ./*,,       Q^/T' 
L-  co         ZTT/  L 

from  which  we  see  that  the  current  in  a  condenser  is  90°  ahead  of 
the  e.m.f.,  and  is  equal  in  value  to  the  current  divided  by  the 
product  of  the  capacitance  and  the  angular  velocity.  The  an- 
gular velocity  is  the  angle  swept  out  in  1  sec.  by  the  re- 
volving vector.  Since  a  complete  revolution  is  equal  to  2ir 
radians  and  since  there  are  /  revolutions  per  second,  we  have 

CO    =    27T/ 

This  will  explain  the  substitution  in  the  above  equations. 

Since  the  e.m.f.  over  the  condenser  and  that  over  the  inductor 
are  exactly  opposed  to  one  another,  it  will  be  seen  that  we  may 
offset  the  effect  of  one  of  these  e.m.fs.  in  a  circuit,  by  the  use 
of  the  other.  Thus  if  the  current  in  a  circuit  lags  behind  the 
e.m.f.,  the  introduction  of  a  condenser  of  the  proper  capacitance 
will  cause  the  current  to  be  in  phase  with  the  e.m.f.  In  practice, 
this  is  most  frequently  done  by  the  employment  of  a  so-called 
synchronous  condenser.  This  is  merely  a  synchronous  motor 
used  for  power-factor  correction.  This  subject  is  fully  discussed 
in  Art.  209. 

The  way  in  which  capacitance  and  inductance  offset  one  another 
will  perhaps  be  most  readily  seen  from  a  consideration  of  the 
mechanical  analogy  of  Fig.  93.  The  forces  required  to  overcome 
inertia  are  greatest  at  the  beginning  of  the  stroke.  At  this  time, 
however,  the  displacement  of  the  water  and  that  of  the  diaphragm 
are  also  greatest.  Consequently  the  force  due  to  the  diaphragm 
is  also  greatest,  and  this  force  is  in  such  a  direction  as  to  tend  to 
start  the  liquid  in  the  direction  in  which  it  is  about  to  move. 
Consequently  it  is  easy  to  see  that  the  one  force  may  partially 
or  entirely  offset  the  other. 

We  are  now  in  a  position  to  derive  the  equation  of  a  circuit 
containing  resistance,  inductance  and  capacitance  in  series. 


INDUCTANCE  AND  CAPACITANCE  151 

Since  the  e.m.fs.  over  the  inductance  and  capacitance  differ  by 
180°,  it  is  evident  that  the  resultant  e.m.f.  of  these  two  will  be 
simply  their  difference  or 


This  resultant  must  be  compounded  with  the  e.m.f.  due  to  the 
resistance  (ER  =  RI),  and  since  this  latter  differs  90°  in  phase 
from  each  of  the  others,  the  resultant  will  be  found  by  extracting 
the  square  root  of  the  sum  of  the  squares  of  the  other  two  or 


This  may  also  be  put  in  the  form 

E 


I  = 


As  before,  E  and  /  may  be  regarded  as  either  maximum  or 
effective  values.  Effective  values  are  usually  employed. 

This  can  be  readily  reduced  to  correspond  to  the  cases  when 
any  one  of  the  three  elements  is  lacking.  Thus  if  there  is  no  in- 
ductance in  the  circuit,  the  value  of  L  is  zero  and  we  get  the  form 

E 


If  there  is  no  condenser  in  the  circuit  it  might  seem  that  we 
should  substitute  zero  for  C.  This  is  not  the  case,  since  as  we 
increase  the  value  of  the  capacitance  the  less  becomes  its  effect. 
Thus  if  the  capacitance  becomes  infinite,  there  will  be  no  drop  of 
potential  over  it  since 

*-«£- 

Ceo 

and  hence  it  will  be  without  effect.  Therefore,  with  an  infinite 
capacitance  in  the  line,  the  conditions  would  be  the  same  as  though 
the  connection  were  made  with  a  solid  conductor  instead  of 
through  the  condenser.  Therefore,  instead  of  substituting  zero 
for  the  capacitance  in  case  no  condenser  is  present,  we  should 
substitute  the  value  infinity. 

This  rather  peculiar  result  will  be  better  understood  from  a 


152      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

consideration  of  the  hydraulic  analogy.  Thus  in  the  latter,  if 
the  diaphragm  is  made  of  infinite  size,  it  will  be  perfectly  flexible 
and  will  therefore  exert  no  force,  and  will  be  entirely  without 
effect  on  the  circuit. 

Making  the  substitution  discussed  above,  we  get  in  the  case  of 
the  circuit  without  a  condenser  the  equation 

E 


This  is  the  same  as  the  expression  we  have  already  derived  in 
Art.  134. 

143.  Resistance,  Reactance  and  Impedance. — We  have  shown 
that  the  general  expression  for  the  current  in  a  circuit  containing 
resistance,  reactance  and  capacitance  is 

7.  * 


This  is  frequently  written 

=       where  X  = 


R  is  the  resistance,  X  is  called  the  reactance  and  the  expression 

Z  = 


is  the  impedance.     The  portion  Leo  of  the  reactance  is  called 

the  inductive  reactance  and  -^~  is   the    condensive  reactance. 

L/co 

The  unit  of  reactance  is  the  ohm. 

144.  Resonance.  —  One  particular  adjustment  of  the  inductive 
and  the  condensive  reactance  in  a  circuit  demands  particular 
attention.  It  will  be  seen  from  the  equation 

E 


that  we  may  readily  adjust  the  capacitance  or  the  inductance  to 
such  a  value  that 


INDUCTANCE  AND  CAPACITANCE 


153 


In  this  case,  the  current  is  given  by  the  same  equation  as  would 
be  used  in  the  case  of  a  continuous-current  circuit,  namely 


R 

with  this  adjustment,  the  circuit  is  said  to  be  in  resonance. 

In  practice,  this  condition  of  resonance  is  of  importance  be- 
cause it  may  lead  to  the  development  of  dangerously  high  poten- 
tials at  various  points  of  a  system.  Thus  in  Fig.  99,  the  applied 
e.m.f.  may  be  220  volts. 

E  =  RI  =  220  volts. 
The  e.m.f.  over  the  inductance  is 

EL 
and  that  over  the  capacitance 


Ceo 

If  the  circuit  is  in  exact  resonance,  EL  and  EC  will  be  equal. 
It  may  readily  occur  that  either  of  them  may  be  far  larger  than 


10       20       30 


40   50   60   70   80   90 
Frequency  in  Cycles 

FIG.  100. 


100     110      120 


the  applied  e.m.f.     This  will  be  particularly  the  case  if  the  re- 
sistance is  low,  and  the  frequency  is  high. 

Resonance  can  also  be  obtained  with  fixed  values  of  the  capaci- 
tance and  inductance,  by  varying  the  frequency.  In  Fig.  100 
are  shown  the  curves  obtained  in  a  test  of  an  actual  circuit.  The 


154      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


inductance  was  constant  and  had  a  value  of  1.0  henry,  and  the 
capacitance  was  likewise  constant  at  7.0  microfarads.  The 
applied  e.m.f.  was  220  volts,  and  the  resistance,  100  ohms. 
Resonance  was  obtained  at  60  cycles,  and  it  will  be  seen  that  the 
e.m.f.  over  the  inductor  and  that  over  the  condenser  were  equal 
and  were  3.77  times  the  applied  e.m.f.  or  830  volts. 

145.  Oscillatory  Discharges.  —  Considering  again  Fig.  93,  sup- 
pose that  the  piston  is  removed  from  the  cylinder,  and  that  the 
diaphragm  is  displaced  to  one  side  and  then  released.  It  is 
evident  that  if  the  friction  of  the  liquid  in  the  tube  is  reasonably 
low,  the  liquid  will  oscillate  for  some  time  instead  of  coming  to 

rest  at  once.     The  curve  of 
current  is  shown  in  Fig.  101. 

This  condition  is  analogous 
to  the  case  of  a  condenser,  in- 
ductor and  resistor  in  series 
without  an  applied  e.m.f.,  i.e., 
with  the  combination  short- 
circuited.  The  connection  is 
shown  in  Fig.  102.  In  either 
the  electric  or  the  liquid  cir- 
cuit, we  have  shown  that  with 
an  applied  alternating  force 
the  greatest  current  will  be 
obtained  when  we  have  the 
condition  of  resonance.  With 

the  short-circuited  electric  circuit,  or  the  hydraulic  circuit  with- 
out the  piston,  the  system  is  not  restricted  to  any  particular  fre- 
quency, and  will  tend  to  oscillate  at  that  frequency  which  will 
give  resonance.  Hence  we  shall  have  the  condition  of  resonance, 
namely, 


FIG.  101. 


Substituting   for  o>  its  value  2irf  and  solving   for  /,  the  fre- 
quency, we  get 

_  J.         1 

/  =  27T  ' 


If  we  desire  that  the  frequency  in  such  a  circuit  be  high,  we 
may  readily  accomplish  our  object  by  making  both  L  and  C 
small.  This  is  the  case  in  wireless  telegraphy.  The  oscillations 


INDUCTANCE  AND  CAPACITANCE 


155 


in  the  sending  circuit  are  obtained  by  means  of  a  circuit  like  that 
of  Fig.  103,  in  which  the  condenser  is  charged  by  a  transformer  and 
allowed  to  discharge  across  a  gap  and  through  the  primary  of  a  high- 


FIG.  102. 


tension,  high-frequency  transformer.  For  wireless  telegraphy,  a 
frequency  of  about  700,000  cycles  per  second  is  customary. 
Since  electric  waves  travel  with  the  velocity  of  light  (186^000 


500,000 


To  Aerial 


High  Tension,  High  Frequency,  Transformer 


60  ~     220V. 

Low  Tension,  Low  Frequency,  Transformer 
FlG.    103. 


miles-  per  second) ,  it  will  be  seen  that  this  corresponds  to  a  wave 
length  of  approximately  ^  mile. 

PROBLEMS 

(Note:  In  the  following,   unless   the   contrary  is  expressly  stated,    all 
currents  and  e.m.fs.  are  supposed  to  be  harmonic.) 


156      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

53.  An  alternating  e.m.f.  of  100  volts  at  a  frequency  of  60  cycles  per  sec- 
ond is  applied  to  a  resistanceless  inductor  of  0.04  henry.     Calculate  the 
current. 

54.  With  the  same  voltage  and  the  same  inductance  as  in  the  above 
problem,  what  would  be  the  necessary  frequency  in  order  that  the  current 
may  be  100  amp.? 

55.  In  a  certain  circuit  the  resistance  is  zero,  the  applied  e.m.f.  is  220 
volts,  the  frequency  is  25  cycles  and  the  current  is  25  amp.     What  is  the 
inductance? 

56.  The  voltage  of  a  circuit  is  440  and  the  current  is  0.01  amp.     What 
is  the  impedance?     If  the  resistance  is  zero,  what  is  the  reactance? 

67.  A  certain  inductive  resistance  has  an  inductance  of  0.01  henry  and 
a  resistance  of  2  ohms.  If  the  voltage  is  220  volts  and  the  frequency  60 
cycles,  what  is  the  current?  What  is  the  power  factor?  What  is  the  angle 
of  lag? 

58.  If  in  the  case  of  the  above  inductor  a  direct  current  of  the  same  value 
were  passed  through  it,  what  would  be  the  e.m.f.  required?    What  would  be 
the  power?     How  does  this  compare  with  the  power  expended  in  the  alter- 
nating-current circuit? 

59.  In  a  certain  circuit  the  power  factor  is  0.6.     R  =  3,  L  =  0.03;  what 
is  the  frequency?     What  would  be  the  frequency  for  unity  power  factor? 
For  zero  power  factor? 

60.  A  certain  condenser  has  a  capacitance  of  2  microfarads.     If  it  is  con- 
nected directly  across  a  220-volt,  60-cycle  circuit  what  will  be  the  current? 
What  would  be  the  current  when  connected  across  a  direct-current  circuit? 

61.  A  condenser  connected  across  60-cycle  mains  takes  a  current  of  1 
amp.,  the  voltage  being  110.     What  is  the  capacitance  of  the  condenser? 

62.  A  condenser  of  a  capacitance  of  1  microfarad  is  connected  in  series 
with  a  non-inductive  resistance  of  1000  ohms.     A  potential  of  250  volts  at 
a  frequency  of  100  cycles  is  applied  to  the  terminals.     What  is  the  current? 
What  is  the  drop  across  the  condenser?     What  is  the  drop  across  the  re- 
sistance?    What  is  the  power  factor?     What  is  the  power? 

63.  A  certain  a.-c.  voltmeter  has  a  resistance  of  1500  ohms  and  zero 
inductance.     When  connected  directly  across  a  60-cycle  circuit  it  reads 
150  volts.     When  it  is  connected  in  series  with  a  condenser  and  the  two  are 
connected  across  the  line  the  reading  is  75  volts.     What  is  the  current  flow- 
ing through  the  voltmeter  and  the  condenser?     Assuming  that  the  line 
voltage  remains  150,  draw  a  vector  diagram  and  compute  the  value  of  the 
e.m.f.  across  the  condenser.      Confirm  this  by  measurement  from  the  dia- 
gram.    From  the  above  compute  the  capacitance  of  the  condenser.     (Note: 
The  preceding  furnishes  a  very  convenient  means  of  measuring  the  capaci- 
tance of  a  condenser,  using  only  a  voltmeter.     The  frequency  of  commercial 
lines  is  usually  known  nearly  enough  and  the  resistance  of  the  voltmeter 
is  usually  given  with  the  instrument.) 

64.  An  harmonic  electric  current  of  100  amp.  flows  through  a  circuit 
consisting  of  a  resistor  of  1  ohm,  an  inductor  of  0.002  henry,  and  a  con- 
denser of  0.00004  farad.     The  frequency  is  60  cycles  per  second.     Draw  a 
vector  diagram  and  compute  the  voltages  across  the  three  elements  of  the 
circuit      Also  compute  the  voltage  across  the  three  in  series.     What  is  the 


INDUCTANCE  AND  CAPACITANCE  157 

power  factor  in  each  of  the  three?     What  is  the  power  factor  of  the  whole 
circuit? 

65.  In  the  case  of  the  foregoing  circuit,  at  what  frequency  would  resonance 
occur?     Answer  the  questions  of  Problem  64  for  the  frequency  of  reson- 
ance. 

66.  A  voltage  of  100  at  a  frequency  of  60  cycles  is  applied  to  a  circuit 
consisting  of  a  non-inductive  resistor  of  5  ohms,  a  reactor  of  0.005  henry, 
and  a  condenser  of   0.00002  farad  in  series.     What  is  the  current?    The 
voltage  across  each  of  the  three  elements  of  the  circuit?     The  power  factor 
of  the  circuit? 

67.  In  the  above,  what  value  of  the  capacitance  will  be  necessary  in  order 
that  the  power  factor  may  be  unity? 

68.  What  is  the  reactance  of  0.24  henry  at  a  frequency  of  60  cycles  per 
second?     What  is  the  reactance  of  a  10-microfarad  condenser  at  the  same 
frequency?     What  is  the  reactance  of  the  two  in  series? 

69.  A  reactance  coil  is  tested  at  60  cycles  with  the  following  results: 
Volts  100,  amperes  5,   watts  173.     Draw  the  vector  diagram.     What  is  the 
power  factor?     The  angle  of  lag?     What  is  the  resistance ?    The  reactance? 
The  impedance?     The  inductance? 

70.  An  harmonic  e.m.f .  of  2200  volts  produces  a  current  of  100  amp.  in  a 
circuit,  the  current  lagging  25°  behind  the  e.m.f.     Calculate  the  resistance, 
reactance  and  impedance. 

71.  A  number  of  incandescent  lamps   taking  100  amp.  of  current  are 
connected  to  an  alternating-current  line.     An  inductive  circuit  of  negligible 
resistance  is  connected  to  the  same  line  and  takes  a  current  of  15  amp. 
What  is  the  total  current  in  the  line? 

72.  An  inductive  resistance  is  connected  across  a  220-volt  60-cycle  line 
and  takes  a  current  of  10  amp.  at  a  power  factor  of  0.7.     A  condenser  is  then 
connected  across  the  line  in  parallel  with  the  inductive  resistance.     What 
must  be  the  capacitance  of  the  condenser  in  order  that  the  power  factor  may 
be  0.85,  the  current  being  lagging?     What  for  unity  power  factor? 

73.  In  a  wireless  telegraph  system  the  capacitance  of  the  aerial  is  1  X 
10~6  microfarads  and  the  inductance  of  the  circuit  is  0.05  henry.     What  is 
the  frequency  of  the  oscillations  in  this  circuit?    What  is  the  wave  length? 


CHAPTER  XIII 
ALTERNATING-CURRENT  MEASURING  INSTRUMENTS 

146.  Action  of  Direct-current   Instruments   on  Alternating- 
current  Circuits. — In  a  previous  chapter  we  have  discussed  some 
forms  of  continuous-current  instruments.     It  will  be  noted  that 
the  instruments  described  in  this  chapter,  while  primarily  designed 
for  use 'on  alternating-current  circuits,  will  nevertheless  in  most 
cases  operate  with  satisfaction  on  direct-current  circuits.     The 
converse  is  not  necessarily  true.     Thus,  an  instrument  of  the 
D'Arsonval  type  if  used  in  connection  with  an  alternating  current 
of  commercial  frequency  will  give  no  deflection.     It  will  have  a 
tendency  to  deflect  first  in  one  direction  and  then  in  the  other, 
but  the  duration  of  the  impulses  is  so  short  that  the  pointer  has 
not  time  to  move  an  appreciable  distance  and  as  far  as  the  eye 
can  detect  does  not  move  at  all.     The  plunger  type  of  instru- 
ment, if  the  moving  plunger  is  of  soft  iron,  may  be  used,  since  the 
plunger  will   be  drawn  into  the  solenoid  no  matter  in  which 
direction  the  current  is  passing. 

147.  The  Electrodynamometer  Type. — An  instrument  of  this 
type  is  shown  in  Fig.  104.     The  construction  is  essentially  the 
same   whether   used    as  a  voltmeter,   ammeter  or   wattmeter. 
This  type  of  instrument  is  common  in  the  highest  grade  and  most 
accurate  forms  of  alternating-current  instruments.     In  general 
it  contains  two  coils,  one  fixed  and  one  movable.     The  fixed  coil 
is  usually  the  larger  and  the  movable  coil  is  arranged  to  rotate 
within  it.     The  axes  of  the  two  coils  are  at  a  considerable  angle 
when  the  instrument  is  carrying  no  current.     For  use  as   an 
ammeter  or  as  a  voltmeter  the  two  coils  are  connected  in  series. 
On  passing  current  through  the  instrument  the  coils  tend  to  turn 
to  such  a  position  that  their  axes  are  parallel.     This  motion  is 
resisted  by  a  spring.     To  understand  this  action  we  may  think 
of  the  stationary  coil  as  taking  the  place  of  the  permanent  magnet 
in  the  D'Arsonval  type  of  instrument.     The  movable  coil  tends 
to  turn  so  as  to  place  its  axis  parallel  to  the  magnetic  lines.     It 
is  evident  that  the  coil  will  turn  in  the  same  direction  no  matter 

158 


AL  TERN  A  TING-C  URREN  T  INSTR  UMEN  TS 


159 


what  the  direction  of  the  current,  since  the  current  is  reversed  in 
both  coils  at  the  same  time.  Moreover,  the  force  acting  on  the 
coil  will  at  all  times  be  proportional  to  the  square  of  the  cur- 
rent, since  the  same  current  passes  through  both  coils.  The  de- 
flection of  the  pointer  will  therefore  be  dependent  upon  the  aver- 
age square  of  the  current,  or  the  instrument  will  indicate  correctly 
irrespective  of  the  wave  shape. 

The  indications  will  also  be  entirely  independent  of  the  fre- 
quency when  the  instrument  is  used  as  an  ammeter.     When 


FIG.  104. 


employed  as  a  voltmeter,  the  current  passing  through  the  instru- 
ment is  given  by  the  expression 


+  (27T/D2 

The  frequency  enters  into  this  expression.  In  order  that  its 
effect  may  be  negligible,  it  is  necessary  that  the  inductance  L 
should  be  made  very  small  in  comparison  with  the  resistance  R. 
Since  a  large  resistance  is  necessarily  used,  and  since  the  induc- 
tance of  the  coils  is  small,  it  is  not  difficult  to  do  this.  Commer- 
cial instruments  give  readings  practically  independent  of  the 
frequency  for  any  of  the  frequencies  in  common  use. 

The  illustration  (Fig.  104)  will  give  an  idea  of  the  internal  con- 
struction of  the  instrument. 

148.  The  Wattmeter.  —  If  connected  as  shown  in  Fig.  105,  the 
electrodynamometer  type  of  instrument  becomes  a  wattmeter. 


160      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


The  stationary  coil  is  wound  with  comparatively  coarse  wire  and 
the  whole  current  passes  through  it.  The  movable  coil  is  wound 
with  fine  wire  and  has  a  large  non-inductive  resistance  connected 
in  series  with  it.  This  coil  is  connected  as  a  shunt  across  the 
line.  The  stationary  coil  has  therefore  passing  through  it  the 
total  current  of  the  circuit.  The  movable  coil  carries  a  current 
proportional  to  the  voltage  of  the  circuit  and  in  phase  with  the 
voltage.  If  the  current  and  the  e.m.f.  in  the  main  circuit  are  in 
phase,  the  currents  in  the  two  coils  are  also  in  phase  and  the  de- 
flection of  the  coil  is  a  maximum  for  the  given  currents.  If,  on 
the  other  hand,  the  current  and  the  e.m.f.  differ  in  phase  by  90°, 

the  current  in  the  movable 
coil  will  be  passing  through 
zero  at  the  instant  when  the 
current  in  the  other  coil  is  a 
maximum.  An  instant  before 
this  takes  place  the  tendency 
to  deflect  will  be  in  one  direc- 
tion and  an  instant  after,  in 
the  opposite  direction,  since 
the  current  has  reversed  in 
only  one  of  the  coils.  The 
time  during  which  the  coil  is 
urged  in  the  one  direction  is 
equal  to  the  time  during 
FIG.  105.  which  it  is  urged  in  the  op- 

posite direction,  and  conse- 
quently the  net  tendency  to  turn  is  zero,  or  no  power  is  indicated. 
This  is  as  it  should  be  since  with  90°  lag  the  power  is  zero. 
Whatever  the  lag  of  the  current,  the  tendency  to  turn  at  any  in- 
stant is  proportional  to  the  instantaneous  power,  that  is,  to  ei, 
and  consequently  the  amount  of  power  is  correctly  indicated. 

149.  Hot  Wire  Instruments. — The  passage  of  current  through 
a  wire  causes  it  to  heat  and  consequently  to  become  longer. 
We  may  use  this  property  to  measure  the  strength  of  the  current. 
One  simple  method  of  doing  this  is  shown  in  Fig.  106.  The  cur- 
rent to  be  measured  is  passed  through  the  wire  W.  Attached 
to  the  center  of  this  wire  is  a  light  flexible  cord  T.  This  passes 
around  the  roller  attached  to  the  pointer  and  is  kept  in  tension  by 
means  of  the  spring  S.  When  current  passes,  W  becomes 
longer,  and  the  spring  acting  on  the  roller  through  the  cord  T  causes 


ALTERNATING-CURRENT  INSTRUMENTS 


161 


the  pointer  to  move  across  the  scale.  It  will  be  apparent  that 
the  movement  of  the  pointer  will  be  great  for  a  comparatively 
small  lengthening  of  the  wire. 

Hot  wire  instruments  may  be  used  either  as  ammeters  or  as 
voltmeters,  a  suitable  resistance  being  used  in  the  latter  case. 
They  may  be  employed  upon  either  continuous-  or  alternating- 
current  circuits.  They  are  not  affected  by  external  magnetic 
fields,  wave  shape,  or,  within  reasonable  limits,  by  frequency. 
The  principal  difficulty  in  the  design  of  these  instruments  seems 
to  be  to  avoid  the  effects  of  the  expansion  of  the  plate,  upon  which 
the  mechanism  is  mounted,  when  the  room  temperature  changes. 


FIG.  106. 


This  causes  the  pointer  to  move  from  the  zero  point.  By  making 
the  base  of  a  material  having  the  same  coefficient  of  expansion  as 
the  wire  the  zero  may  be  made  reasonably  stable. 

Hot  wire  instruments,  particularly  in  the  case  of  ammeters, 
having  thick  wires,  are  naturally  somewhat  sluggish,  that  is,  it 
requires  some  time  for  the  wire  to  heat  up  to  its  final  temperature. 
This  may  be  a  disadvantage  in  certain  applications,  but  it  may 
also  be  advantageous  in  case  we  wish  to  measure  a  current  which 
is  rapidly  fluctuating.  The  current  in  the  armature  of  a  lightly 
loaded  synchronous  motor  is  frequently  unsteady  and  sometimes 
the  hot  wire  instrument  is  the  only  one  which  will  give  a  readable 
deflection, 
n 


162      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY      . 

150.  The  Spark  Gap. — Very  high  voltages  are  frequently  best 
measured  by  means  of  a  spark  gap.     Two  sharp  needles  or  two 
spheres  of  a  definite  diameter  are  used.     The  distance  between 
the  needle  points  when  the  current  jumps  is  a  measure  of  the  volt- 
age across  the  gap.     Very  careful  measurements  have  been  made 
of  the  properties  of  spark  gaps  and  it  is  possible  with  the  aid  of  a 
curve  to  estimate  quite  closely  the  voltage  of  the  circuit.     It 
must,  however,  be  remembered  that  the  breakdown  of  the  gap  is 
dependent  upon  the  maximum  value  of  the  voltage  and  not  upon 
the  effective  value. 

151.  The   Electrostatic   Voltmeter. — If  two  insulated   metal 
plates  are  at  different  potentials  they  will  attract  one  another 
with  a  force  proportional  to  the  square  of  the  difference  of  poten- 
tial.    This  force  may  be  measured  by  noting  the  deflection  of  a 
spring  or  otherwise,  and  will  be  a  measure  of  the  e.m.f.     Either 
direct  or  alternating  e.m.fs.  may  be  measured.     The  instruments 
are  particularly  adapted  to  voltages  of  1000  or  over  although  they 
are  also  built  for  lower  voltages. 

It  will  be  noted  that  both  of  the  last  two  instruments  described 
are  inherently  voltmeters,  while  all  the  others  are  inherently 
ammeters. 

152.  The  Oscillograph. — In  the  study   of    alternating-current 
phenomena  it  is  important  to  be  able  to  follow  the  fluctuations  of 
the  current  or  the  voltage  as  it  passes  through  its  cycle.     Since  a 
complete  cycle  requires  usually  only  3^5  or  J^Q  of  a  second,  it  will 
be  apparent  that  this  is  difficult  to  accomplish.     If  it  required, 
say,  an  hour  to  complete  a  cycle,  the  fluctuations  of  the  current 
or  the  e.m.f.  could  be  readily  followed  by  means  of  a  continuous- 
current  instrument,  the  zero  being  preferably  in  the  middle  of  the 
scale.     With  a  frequency  of  1    cycle   per   second,  the   pointer 
would  begin  to  lag  somewhat  behind  the  current  or  e.m.f.  and 
at,  say,  25  cycles  per  second  there  would  be  little  or  no  deflection, 
since  the  negative  impulses  would  equal  the  positive,  and  since 
the  pointer  would  not  have  time  to  move  between  them. 

If,  however,  the  pointer  and  other  moving  parts  be  made  very 
light,  they  will  be  capable  of  keeping  up  with  the  variations  of 
the  current  at  a  higher  frequency,  and  by  going  to  extreme  light- 
ness, we  may  construct  an  instrument  capable  of  following 
accurately  the  variations  of  a  current  of  any  commercial  fre- 
quency. Figure  107  illustrates  the  construction  employed.  A 
very  fine  wire  is  held  in  the  shape  of  a  loop  between  the  poles  of 


AL  TERN  A  TING-C  URREN  T  INSTR  UMEN  TS 


163 


a  magnet.  Across  the  loop  is  cemented  a  light  mirror.  A  beam 
of  light  reflected  from  the  mirror  is  used  as  the  pointer.  When 
current  passes  through  the  loop,  one  side  is  pushed  forward  by  the 
action  of  the  current  in  the  magnetic  field  while  the  other  side  is 
pressed  backward.  As  a  consequence  the  mirror  is  twisted 
through  a  small  angle  and  the  beam  of  light  is  deflected. 

The  movements  of  the  beam  of  light  may  be  recorded  by  allow- 
ing it  to  trace  its  path  upon  a  falling  photographic  plate.  As 
an  alternative  we  may  use  a  film  wrapped  upon  a  rotating  cylin- 
der. Figures  69,  70,  71,  and  72  show  curves  obtained  in  this  way. 


FIG.  107. 

We  may  also  examine  the  shape  of  the  wave  without  the  neces- 
sity of  photographing  it  by  allowing  the  beam  of  light  to  fall 
upon  a  mirror  rocked  through  a  small  angle  by  a  synchronous 
motor.  The  motor  should  be  driven  from  the  circuit  to  be  inves- 
tigated, and  the  motion  of  the  synchronous  mirror  should  be 
such  as  to  deflect  the  beam  of  light  at  right  angles  to  the  deflection 
due  to  the  current.  A  shutter,  also  actuated  by  the  synchronous 
motor,  should  cut  off  the  light  during  the  return  of  the  beam. 
Under  these  conditions,  the  spot  of  light  will  trace  out  the  same 
curve  repeatedly,  and  since  the  eye  can  not  follow  the  rapid 
movement  of  the  spot  of  light,  the  curve  will  appear  to  be 
stationary  upon  the  screen.  It  can  then  be  readily  examined 
or  traced  for  preservation. 


CHAPTER  XIV 
SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 

153.  Alternating- Current  Generators. — Alternating-current 
generators,  motors  and  transmission  lines  are  usually  single,  two 
or  three  phase,  although  systems  with  a  greater  number  of  phases 
are  occasionally  used.  Figure  108  shows  the  essential  elements 
of  a  single-phase  synchronous  generator  or  motor.  This  machine 
has  a  stationary  armature  and  a  field  revolving  within  it.  It  is 
much  easier  to  insulate  a  stationary  armature,  and  the  fact  that 
it  is  not  necessary  to  use  slip  rings  to  convey  the  current  from  the 


armature  to  the  outside  circuit  makes  the  machine  cheaper  to 
construct.  For  these  reasons  the  older  type  of  revolving  arma- 
ture alternator  is  practically  obsolete. 

The  armature  in  this  case  is  provided  with  24  slots  or  6  slots 
per  pole.  In  practice  the  number  of  slots  per  pole  may  vary 
from  3  to  18  or  more.  Of  the  24  slots  only  16  have  conductors 
in  them,  the  remainder  being  left  vacant.  The  old  type  of  al- 
ternator, in  which  only  1  slot  per  pole  was  used,  is  obsolete.  The 
idea  underlying  the  connection  of  the  conductors  is  exceedingly 
simple  although  it  frequently  leads  to  somewhat  complex  dia- 

164 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


165 


grams.  //  the  conductors  are  so  connected  that  the  passage  of  con- 
tinuous current  through  the  winding  gives  a  series  of  bands  of  current, 
all  the  currents  in  a  band  flowing  in  the  same  direction,  the  connection 
will  be  correct.  One  way  of  doing  this  is  shown  in  Fig.  109.  If 
we  start  at  the  terminal  marked  +  and  follow  through  the  wind- 
ing to  the  terminal  marked  — ,  it  will  be  seen  that  the  arrows 
indicate  correctly  the  direction  of  a  continuous  current  passing 
through  the  winding.  There  is  first  a  band  of  four  conductors 
with  the  current  in  the  same  direction  in  all  of  them,  then  a 
band  with  all  the  currents  in  the  opposite  direction,  and  so  on. 
The  field  is  excited  with  continuous  current.  When  the  rela- 
tive positions  of  the  field  and  armature  are  those  shown  in  Fig. 
108,  with  clockwise  rotation,  an  e.m.f.  will  be  induced  in  con- 
ductors 2,  3,4,  and  5  and  in  14,  15,  16,  and  17  directed  from  the 
observer,  with  the  direction  of  rotation  as  shown.  In  conductors 


FIG.  109. 

8,  9,  10,  and  11,  and  20,  21,  22,  and  23,  the  e.m.f.  will  be  in 
the  opposite  direction.  These  conductors  are  to  be  connected 
in  series  with  one  another  in  such  a  manner  that  their  e.m.fs. 
will  all  add  together,  and  all  assist  the  current  to  flow.  This 
will  be  the  case  if  the  rule  already  stated  is  adhered  to,  as  will 
be  apparent  from  Fig.  109. 

In  the  alternator  just  described  one-third  of  the  slots  have  been 
left  vacant.  There  is  nothing  to  prevent  us  from  placing  coils 
in  these  slots  and  connecting  these  coils  in  series  with  the  rest  of 
the  winding.  The  gain  in  e.m.f.  from  these  coils  would  however 
be  small.  Thus  a  coil  in  slots  6  and  7,  would  embrace  onry  a 
small  portion  of  the  flux  from  a  pole  and  would  generate  only  a 
small  e.m.f.  Omission  of  the  coils  in  slots  6  and  7,  12  and  13, 
18  and  19,  and  24  and  1  as  shown  in  Fig.  109  reduces  the  generated 
voltage  13.4  per  cent.,  but  saves  approximately  30  per  cent,  of 


166      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

the  copper  used  on  the  armature.  In  addition  to  increasing  the 
cost,  the  use  of  these  coils  would  result  in  a  lowering  of  the 
efficiency,  and  in  a  poorer  regulation.  For  this  reason  they  are 
rarely  used  in  a  single-phase  alternator. 

As  stated,  the  field  of  an  alternator  is  excited  by  means  of 
continuous  current.  This  is  usually  supplied  by  a  small  direct- 
current  generator.  If  only  one  or  two  alternators  are  to  be 
installed  in  a  given  station,  the  exciters  may  be  belted  or  direct- 
connected  to  the  main  generators.  In  larger  stations,  it  is  cus- 
tomary to  drive  the  exciters  from  individual  prime  movers 
(usually  steam  engines  or  water  wheels),  or  by  means  of  alternat- 
ing-current motors,  taking  their  current  from  the  main  generators. 


FIG.  110. 


In  addition,  in  large  stations  a  storage  battery  is  usually  provided 
as  insurance  against  failure  of  exciting  current,  and  to  supply 
current  for  the  station  lights  in  case  of  a  complete  shutdown. 

154.  The  Two-phase  Generator. — We  have  pointed  out  that 
in  the  single-phase  generator  it  is  advisable  to  use  only  about 
two-thirds  of  the  slots,  the  remaining  third  being  vacant.  By 
thus  leaving  out  one-third  of  the  coils  we  lose  about  13  per  cent, 
in  voltage  and  save  nearly  30  per  cent,  in  the  amount  of  armature 
copper.  We  may  go  a  step  farther  and  use  only  half  of  the  slots. 
By  doing  this  we  lose  30  per  cent,  in  voltage  and  save  50  per  cent, 
in  armature  copper.  A  winding  of  this  character  is  shown  by  the 
full  lines  of  Fig.  110.  This  winding  is  of  a  different  type  from 
that  of  Fig.  109.  There  are  two  coil  sides  in  each  slot  instead  of 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


167 


one,  and  the  coils  are  all  alike.  This  is  advantageous  from  the 
manufacturing  standpoint  and  at  the  same  time,  makes  it  easier 
for  the  user  to  carry  spare  coils  in  case  of  a  breakdown.  By  trac- 
ing through  the  winding  it  will  be  evident  that  we  have  followed 
the  same  principle  as  in  Fig.  109,  namely,  that  when  current 
passes  through  the  armature  a  number  of  bands  of  current, 
having  alternately  opposite  directions,  are  formed. 


FIG.  111. 


In  a  single-phase  machine  we  would  usually  make  use  of  a 
greater  percentage  of  the  slots  than  one-half,  although  we  could 
use  only  one-half  of  them  with  comparatively  little  loss.  How- 
ever, if  we  have  only  half  of  the  slots  occupied  it  would  at  once 
appear  that  we  could  readily  wind  a  second  winding  in  the  vacant 
slots  and  thus  double  the  capacity  of  our  alternator  at  the  ex- 
pense of  doubling  the  armature  copper, 
everything  else  remaining  the  same.  The 
capacity  of  the  generator  would  be  41  per 
cent,  greater  than  that  of  the  same  machine 
wound  single  phase,  with  all  the  slots  used,  j 

With  this  connection,  the  e.m.fs.  of  the 
two  phases  differ  by  90°,  that  is,  when  one 
e.m.f.  is  a  maximum  the  other  is  zero 
and  vice  versa.  The  e.m.f.  of  the  A  phase 
is  a  maximum  when  the  center  of  the  pole 
is  opposite  the  band  of  conductors  marked  A.  At  this  same 
time  the  B  band  of  conductors  is  opposite  the  space  between 
two  poles  and  consequently  no  voltage  is  generated  in  the  B 
winding.  The  two  e.m.fs.  may  be  represented  by  the  curves  of 
Fig.  Ill,  or  by  the  vectors  A  and  B  of  Fig.  112. 

This  figure  also  serves  to  explain  why  more  capacity  can  be 
obtained  from  the  machine  connected  two  phase  than  when  con- 
nected single  phase.  If  we  should  connect  the  two  windings  in 


B 
FIG.  112. 


168      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

series  the  combination  would  constitute  a  single-phase  winding. 
The  e.m.f.  would  be  the  vector  sum  of  the  two  separate  e.m.fs. 
and  would  be  represented  by  the  line  marked  A  +  B  in  Fig. 
112.  If  we  take  A  and  B  as  each  being  equal  to  1,  A  +  B  will  be 
equal  to  \/2  =  1.41.  We  may  assume  without  serious  error  that 
each  winding  will  carry  the  same  current  whether  connected 
single  or  two  phase,  or  the  capacities  will  be  proportional  to  the 
voltages.  The  rating  of  the  single-phase  machine  may  then  be 
taken  as  1.41  while  the  rating  of  the  two-phase  machine  would 
be  2  or  41  per  cent,  greater. 

155.  Electromotive  Force  of  an  Alternator.  —  In  an  alternator 
the  flux  through  a  coil  is  represented  at  any  instant  by  the  ex- 
pression, 

<p  =  $  sin  cot 

Where  <I>  is  the  maximum  value  of  the  flux  passing  through  one 
armature  coil.  The  instantaneous  e.m.f.  induced  in  the  arma- 
ture winding  is  given  by 


N    d<p 

-WTt~-      To^ 

where  N  is  the  number  of  turns  (i.e.,  half  the  number  of  conduct- 
ors) converted  in  series.     The  maximum  value  of  the  e.m.f.  is 

and  the  effective  value  is 


—      n 

E_*M_W*__ 

V2       \/2  X  108 

With  a  distributed  winding  as  ordinarily  used  the  maximum 
e.m.f.  does  not  occur  in  all  the  coils  at  the  same  time.  To  allow 
for  this  we  multiply  by  a  factor  called  the  breadth  coefficient. 
This  varies  slightly  with  different  windings  but  is  very  nearly 
0.95  for  three-phase  windings  and  0.90  for  two  phase. 

156.  Method  of  Connecting  Load.  —  The  connection  of  a  two- 
phase  alternator  to  its  load  is  shown  in  Fig.  113.  The  two  cir- 
cuits are  usually  entirely  independent  of  one  another,  although  in 
some  cases  they  are  interconnected  as  will  be  shown  presently. 
To  supply  lights  we  should  run  two  wires  to  each  group  exactly 
as  though  they  were  to  be  operated  from  a  single-phase  generator. 
In  order  that  the  voltages  may  not  differ  too  much  it  is  desirable 
that  the  loads  on  the  two  circuits  be  nearly  the  same.  Thus  if  a 
system  were  being  operated  single  phase  and  we  wished  to  change 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


169 


to  two  phase,  it  would  merely  be  necessary  to  divide  the  load  into 
two  fairly  equal  parts  and  connect  the  parts  to  the  two  phases. 
Small  single-phase  motors  might  be  operated  from  one  phase,  but 
in  general,  the  motors  would  be  wound  for  two-phase  operation, 
and  it  would  therefore  be  necessary  to  run  all  four  wires  to  each 
of  them. 


6666 


6666 


FIG.  113, 

In  the  foregoing  we  have  shown  the  phases  as  entirely  insulated 
from  one  another.  There  is  however  nothing  to  prevent  us  from 
connecting  any  one  point  on  either  winding  to  any  one  point  on 
the  other.  Since  there  would  be  only  the  one  connection,  there 
would  be  no  circuit  between  the  two  windings  and  no  current 
could  flow  through  the  connection.  The  operation  of  each  wind- 
ing would  therefore  be  the  same  as  before. 


100  Volts 


100  Volte 


141.4  Volts 


FIG.  114. 

Thus  we  might  connect  the  ends  of  the  windings  together  as 
shown  in  Fig.  114.  If  each  winding  developed  100  volts  we 
should  have  this  pressure  between  wires  A  and  B  and  between  B 
and  C,  while  between  A  and  C  there  would  be  141  volts.  This 
connection  may  be  used  in  special  cases  but  in  general  it  possesses 
no  particular  advantage  and  is  rarely  used. 


170      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


A  more  common  connection  is  that  of  Fig.  115,  in  which  the 
middle  points  of  the  two  windings  are  connected.  In  this  case 
if  each  winding  generates  100  volts,  we  can  make  four  additional 
connections  giving  in  each  case  70.7  volts  or  half  of  that  between 
A  and  C  in  Fig.  114. 


100  Volts  I 
I      70.7.  Volts 


70.7  Volts 


100  Volts 

I i 


70.7  Volts 


70.7V 


bits 


FIG.  115. 


157.  Three-phase  Systems. — It  has  been  shown  that  by  using 
the  two-phase  system  we  can  obtain  a  considerably  greater  out- 
put from  a  given  generator  than  would  be  possible  with  single- 
phase  operation.  By  using  a  three-phase  connection  it  is  pos- 


FIG.  116. 

sible  to  increase  the  power  output  about  5  per  cent,  above  that  of 
a  two-phase  generator.  There  is  also  a  distinct  advantage  in 
transmission.  Three  wires  in  a  three-phase  system  will  trans- 
mit a  certain  amount  of  power  at  a  given  voltage  with  the  same 
loss  as  would  be  present  in  four  wires  of  the  same  size  in  a  two- 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


171 


phase  transmission.  These  and  other  advantages  have  caused 
the  three-phase  system  to  be  preferred  in  most  cases.  It  may 
be  considered  the  standard  method  of  alternating-current  genera- 
tion and  distribution. 

A  diagram  of  a  three-phase  winding  is  shown  in  Fig.  116.     One 
phase  is  represented  by  means  of  heavy  lines,  the  second  by  a  light 


FIG.  117. 


FIG.  118. 


line  and  the  third  by  means  of  a  broken  line.  Since  each  band 
spans  a  distance  of  one-third  of  a  pole  pitch,  each  winding  will 
differ  in  phase  from  its  neighbor  by  60°.  This  relation  is  shown 
in  Fig.  117.  This  connection  gives  an  unsymmetrical  e  m.f.,  and 
to  obtain  a  three-phase  connection  it  is  necessary  to  reverse  the 
connections  of  the  middle  phase.  We  then  have  the  relation 


FIG.  119. 

shown  in  Fig.  118,  or  a  difference  of  phase  of  120°.  The  corre- 
sponding curves  plotted  in  rectangular  co-ordinates  are  shown  in 
Fig.  119. 

158.  Advantages  of  Three  Phase  over  Single  Phase. — To 
show  the  advantage  of  the  three-phase  connection  over  the  single 
phase  we  may  connect  the  three  phases  in  series  to  form  a  single- 
phase  winding.  There  are  two  possible  ways  of  doing  this. 


172      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


One  would  be  represented  by  the  vector  diagram  of  Fig.  120.  The 
sum  of  A  and  B  is  equal  in  magnitude  to  either  A  or  B  or  to  C. 
Adding  C  in  the  phase  shown  just  neutralizes  the  sum  of  A  and  B 
or  the  total  sum  is  zero.  By  reversing  the  connection  of  C, 
however,  we  obtain  a  relation  represented 
by  Fig.  121  in  which  the  total  voltage  is 
exactly  twice  the  voltage  of  any  one  phase. 
Operated  three  phase  we  get  the  full  voltage 
of  each  phase.  We  may  therefore  conclude 
that  if  the  output  of  a  single-phase  gener- 
ator in  which  all  of  the  slots  are  used  is 
represented  by  2,  the  output  of  the  same 
machine  wound  three 
phase  would  be  3,  or 
an  advantage  of  50  per 
cent,  in  favor  of  the 
three-phase  machine. 
As  we  have  previ- 
ously shown,  we 
would,  in  general,  in 
a  single-phase  ma- 
chine use  only  about 

two-thirds  of  the  slots,  the  remainder  being  left  vacant.  We 
can  readily  show  the  exact  loss  of  capacity  involved  by  means  of 
a  vector  diagram.  If  we  should  use  only  two  of  the  three  wind- 
ings of  a  three-phase  machine  in  a  single-phase  machine  we  could 
connect  them  in  such  a  manner  as  to  give  a  vector  diagram  the 

same  as  that  of  Fig.  121  if  C  were 
omitted.  The  voltage  would  then  be 
that  of  one  phase  only  or  might  be  repre- 
sented by  1.  This  would  obviously  be 
undesirable,  and  the  machine  can  be 
very  much  improved  by  reversing  the 

connections  of  the  B  phase  giving  the  vector  diagram  shown  in 
Fig.  122.  It  will  be  seen  that  the  angles  between  A  and  B  and 
the  resultant  are  in  both  cases  equal  to  30°.  The  resultant  will 
be  given  by  the  expression 


FIG.  120. 


FIG.  121. 


A  +B 


FIG.  122. 


A  +  B  =  2A  cos  30°  =  2 


\x 

X  ~2~ 


=  1.73  A 


Since  if  all  three  windings  are  used  we  obtain  a  voltage  of  2A, 
there  is  an  increase  of  approximately  15  per  cent,  in  voltage  if 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


173 


three  windings  instead  of  two  are  used.  As  previously  pointed 
out,  three  windings  require  50  per  cent,  more  copper,  and  involve 
50  per  cent,  more  RI2  loss.  The  increase  in  voltage  is  hardly 
enough  to  pay  for  the  disadvantage  and  consequently  only  about 
two-thirds  of  the  slots  are  ordinarily  used,  in  a  single-phase 
generator  or  motor. 

159.  Three-phase  Connections. — The  most  obvious  method 


Three  Phase 
Motor 

FIG.  123. 


Single  Phase 
Motor 


of  connecting  a  three-phase  alternator  to  its  load  would  be  to 
run  three  independent  circuits  of  two  wires  each.  This  is  rarely 
or  never  done  except  in  the  case  of  rotary  converters,  since  it 
involves  the  use  of  six  wires,  six  pole  switches,  six  pole  cut-outs, 
etc.  Such  an  arrangement  would  be  known  as  a  six-phase 
system. 


FIG.  124. 

Two  methods  of  connection  are  in  general  use.  These  are 
illustrated  in  Figs.  123  and  124  and  are  known  respectively  as 
the  star  or  "Y"  connection  and  the  delta  or  mesh  connection. 
The  corresponding  vector  diagrams  are  given  in  Figs.  125  and 
126.  With  either  of  these  connections  it  will  be  evident  that  all 
the  voltages  from  A  to  B,  from  B  to  C,  and  from  C  to  A  will  be 


174      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


the  same  in  magnitude  but  will  differ  120°  in  phase.  We  can 
therefore  connect  single-phase  apparatus  across  any  one  of  these 
three  circuits  as  shown  in  Fig.  123.  Apparatus  requiring  three- 
phase  current  such  as  induction  motors,  may  be  connected  to  all 
three  lines. 

Fig.  125  requires  a  little  further  explanation  in  order  that  it 
may  be  entirely  clear.  The  vectors  A,  B  and  C  have  all  been 
drawn  as  being  directed  outward  from  the  center,  that  is,  the 
voltage  A  is  considered  as  being  positive  when  its  direction  is 
from  the  neutral  point  outward  and  likewise  with  the  other 
e.m.fs.  If  we  consider  a  current  passing  from  the  point  c  to  the 
point  a,  it  will  be  evident  that  a  positive  direction  of  the  e.m.f. 
in  the  winding  A  will  help  the  passage  of  the  current  while  a 
positive  e.m.f.  in  C  will  oppose  it.  At  the  instant  shown  we  may 
consider  that  A  has  its  maximum  positive  value  while  C  is  nega- 


FIG.  125. 


c 
FIG.  126. 


tive.  Both  e.m.fs.  will  therefore  help  the  passage  of  the  current. 
In  considering  the  effect  of  the  e.m.f.,  C,  upon  the  current  it  will 
therefore  be  necessary  to  consider  it  as  being  negative.  The 
vector  CA  is  therefore  the  vector  sum  of  A  and  —  C.  Likewise, 
AB  is  the  vector  sum  of  B  and  —  A,  and  BC  the  vector  sum  of 
C  and  -  B. 

160.  Voltage  and  Current  Relations. — With  the  star  connecti.on 
(Fig.  123)  the  current  in  any  one  of  the  three  generator  windings 
is  obviously  the  same  as  the  current  in  the  corresponding  line 
wire,  since  the  two  are  directly  connected  in  series.  The  voltage 
between  any  two  line  wires,  however,  is  not  the  voltage  of  one 
of  the  generator  windings.  If  we  represent  the  line  voltage, 
CA  by  E,  and  the  voltage  of  one  generator  phase,  A  by  Eg,  it 
will  be  evident  from  Fig.  125  that 

E  =  2Eg  cos  30°  =VZE0  =  1.73  Eg 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS  175 

With  the  mesh  connection  of  Fig.  124,  it  will  be  seen  that  the 
line  voltage  is  the  same  as  that  of  one  generator  winding.  The 
line  current  will,  however,  be  the  vector  sum  of  the  currents  in 
the  two  generator  windings  connected  to  the  line  wire.  If  the 
two  currents  are  the  same,  the  process  of  finding  their  resultant 
will  be  the  same  as  that  of  finding  the  resultant  of  the  two  vol- 
tages of  Fig.  123,  since  they  are  at  the  same  angle  to  one  another 
as  the  two  voltages.  Designating  the  line  current  by  I  and  the 
generator  current  per  phase  by  Ig  we  have 

/  =  Y/3/,  =  1.737, 

161.  Power  in  Balanced   Three-phase  Circuits. — If  we  con- 
sider one  of  the  windings  in  Fig.  123  or  Fig.  124,  it  will  be  evident 
that  the  power  in  this  winding  is  equal  to  the  current  times  the 
e.m.f.  times  the  power  factor.     The  total  power  of  the  generator 
will  be  the  sum  of  the  power  of  the  three  phases.     This  will  be 
true  for  either  balanced  or  unbalanced  loads.     For  balanced 
loads  we  may  write  for  the  star  connection 

P  =  3EgI  cos  0  =  \/3EI  cos  0 

where  P  is  the  power  output  of  the  three  phases  and  cos  0  is  the 
power  factor.  A  simple  substitution  will  give  the  same  result 
for  the  mesh  connection. 

162.  Substitution  of  a  Three-phase  Alternator  for  a  Single- 
phase  Machine. — When  a  piece  of  apparatus  is  connected  to  a 
line  so  as  to  take  current  from  it,  the  voltage  of  the  line  will  in 
general  be  changed,  and  will  usually  be  lowered.     It  is  therefore 
advisable  that  the  current  taken  from  the  three  circuits  be  the 
same,  both  in  quantity  and  in  the  angle  of  lead  or  lag,  so  that  the 
three  voltages  may  remain  balanced.     However,  it  is  by  no  means 
necessary  that  this  be  done,  provided  a  small  unbalancing  of  the 
three  voltages  is  not  objectionable.     Thus  all  the  load  might  be 
connected  between  the  lines  A  and  B.     The  winding  C  would 
then  carry  no  current  and  the  machine  would  operate  as  a  single- 
phase  alternator;  or  we  might  connect  all  the  lighting  load  across 
A  and  B,  running  the  third  wire  C  only  to  whatever  three- 
phase  motors  might  be  connected  to  the  system.     The  unbalanc- 
ing of  the  voltage  on  the  motors,  while  somewhat  undesirable, 
might  not  be  serious.     This  expedient  is  sometimes  used  when 
it  is  desirable  to  add  a  motor  load  to  an  established  single-phase 
system.     A  three-phase  generator  may  be  purchased,  the  lights 


176      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

operated  as  before  from  one  phase,  and  all  three  wires  run  to  such 
motors  as  may  be  installed. 

163.  Rotating  Magnetic  Field  in  the  Armature  of  the  Alter- 
nator.— Figure  108  shows  a  section  of  a  revolving  field  alternator. 
In  discussing  this  machine  it  was  assumed  that  all  of  the  magnetic 
field  was  produced  by  the  action  of  the  field  magnet.     This  is 
not  the  case,  as  the  armature  current  has  a  considerable  effect 
upon  the  magnetism.     In  the  single-phase  alternator  the  arma- 
ture current  has  a  tendency  to  cause  the  field   magnetism  to 
pulsate.     In  the  two-  or  three-phase  machine,  the  effect  is  prac- 
tically constant  and  tends  either  to  weaken  or  to  strengthen  the 
magnetism  which  would  be  present  due  to  the  field  alone. 

Referring  to  either  Fig.  108  or  Fig.  109,  it  will  be  seen  that  if 
a  continuous  current  be  passed  through  the  winding  of  the  arma- 
ture in  the  direction  shown,  four  poles  will  be  formed  on  the 
armature  surface.  The  strength  of  these  poles  will  be  greatest 
in  the  positions  indicated  and  will  gradually  diminish  in  strength 
to  the  positions  half  way  between  the  points  marked.  There 
will  thus  be  a  gradual  shading  off  from  one  pole  to  the  next. 

164.  Action  with  Single -phase  Alternating  Current. — If  a  sin- 
gle-phase alternating  current  be  passed  through  the  winding  de- 
scribed, poles  will  be  formed  as  with  the   continuous  current, 
but  these  poles  will  die  out  and  reverse  in  phase  with  the  current. 
In   other  words,  the   field  is  stationary  in  space  and  pulsat- 
ing in  value.     If  the  field  magnet  is  within  the  armature  and  the 
machine  itself  is  generating  the  current  which  passes  through  the 
armature,  the  same  considerations  will  hold.     The  effect  of  the 
armature  current  upon  the  field  magnetism  is,  then,  to  cause  it 
to  pulsate  somewhat  in  value.     If  the  current  delivered  by  the 
alternator  is  neither  lagging  nor  leading,  there  will  be  but  little 
effect   upon   the    average    value    of   the    magnetism    since   the 
armature  exerts   its  strongest  effect  midway  between  the  field 
poles.     If  the  current  is  lagging  it  will  have  a  powerful  tend- 
ency to  weaken  the  field,  and  conversely  if  it  is  leading  it  will 
strengthen  the  field.     This  effect,  known  as  armature  reaction, 
will  be  more  fully  treated  in  the  chapter  upon  the  synchronous 
machine. 

165.  Action  with  Two-phase  Alternating  Current. — If  but  one 
winding  only  of  the  two-phase  armature  of  Fig.  110  is  considered, 
it  wil]  be  seen  that  an  alternating  current   passed  through  it 
would  have  the  same  effect  as  that  just  described.     If  an  alter- 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS  177 

nating  current  were  passed  through  the  other  winding,  the  effect 
would  be  the  same  except  that  the  poles  would  be  shifted  to  a 
position  midway  between  those  due  to  the  first  winding.  If  a 
single-phase  current  were  passed  through  both  of  these  windings 
in  series,  the  two  sets  of  poles  would  unite  to  form  a  resultant  set 
of  poles  midway  between  the  other  two  sets. 

If,  however,  currents  differing  in  phase  by  90°  (that  is,  so  re- 
lated that  when  one  current  is  a  maximum  the  other  is  zero) 
are  passed  through  the  two  phases,  the  action  is  quite  different. 
Thus  in  Fig.  110,  at  the  time  when  the  current  in  the  A  phase 
is  a  maximum  in  the  direction  shown  the  maximum  points  of 
the  north  poles  will  be  opposite  slots  11  and  23,  and  those  of  the 
south  poles  opposite  5  and  17.  A  quarter  of  a  period  later  the 
current  in  the  A  phase  will  be  zero  and  that  in  the  B  phase  a 
maximum.  The  poles  will  then  be  opposite  the  slots  2,  8,  14, 
and  20,  or  in  other  words,  the  poles  have  moved  three  slots  or 
one-half  of  a  pole  pitch  to  the  right. 

If  the  condition  at  a  time  intermediate  between  the  two  times 
noted  above  is  considered,  namely,  when  the  two  currents  are 
equal  as  shown  at  time  2  of  Fig.  Ill,  it  will  be  evident  that 
both  windings  will  have  an  effect  and  resultant  poles  will  be 
formed  midway  between  those  due  to  each  winding  alone. 

From  the  foregoing  it  appears  that  the  poles  will  travel  along 
the  face  of  the  armature  at  a  practically  uniform  rate  of  speed 
and  that  the  strength  of  the  poles  will  be  practically  constant. 
The  speed  will  be  such  that  a  distance  equal  to  twice  the  pole 
pitch  will  be  passed  over  during  1  cycle.  Since  the  poles  of  the 
field  magnet  also  travel  at  the  same  rate,  the  field  due  to  the 
armature  and  that  due  to  the  field  magnet  will  maintain  the 
same  relative  position,  as  long  as  the  conditions  do  not  change. 

166.  Action  with  a  Three-phase  Current. — In  a  like  manner 
with  the  aid  of  Figs.  116  and  120  one  can  trace  the  magnetizing 
action  of  a  three-phase  current  upon  the  armature.     It  will  be 
found  that  at  all  times  at  least  two  of  the  phases  are  carrying 
current  and  most  of  the  time  all  of  the  phases  are  active.    -The 
speed  of  the  field  will  be  the  same  as  before,  and  consequently 
the  same  as  the  speed  of  the  field  magnet.     This  fact  would  be 
true  for  any  number  of  phases. 

167.  The  Synchronous  Motor. — The  foregoing  considerations 
lead  to  seeing  in  a  simple  manner  how  an  alternator  may  act  as 
a  motor.     Assume  that  the  armature  of  the  alternator  repre- 

12 


178      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

sented  in  Fig.  108  is  wound  for  either  two-  or  three-phase  opera- 
tion and  that  the  corresponding  two-  or  three-phase  current  is 
passed  through  it.  A  revolving  magnetic  field  will  be  set  up  as 
previously  indicated.  Rotate  the  field  magnet  by  external  power 
at  the  same  speed  as  the  revolving  magnetic  field,  and  remove 
the  driving  power.  Even  though  there  is  no  current  in  the  field 
windings,  the  revolving  magnetism  of  the  armature  will  attract 
the  poles  of  the  field  as  any  magnet  attracts  soft  iron,  and  will 
carry  the  poles  around  with  it.  The  machine  will  then  act  as  a 
motor  and  will  continue  to  revolve  at  exactly  this  same  speed  as 
long  as  the  frequency  of  the  current  supplied  remains  the  same. 
Variations  of  voltage,  current,  changes  in  the  load,  etc.,  will  have 
absolutely  no  effect  upon  the  speed,  provided  that  the  load  doesnot 
become  so  great  or  the  voltage  so  low  that  the  machine  is  unable 
to  carry  the  load.  If  this  is  the  case,  the  motor  will  stop  entirely. 

The  passage  of  current  through  the  field  coils  will  strengthen 
the  attraction  between  the  field  and  armature  and  enable  the 
machine  to  carry  more  load  without  "  dropping  out  of  step," 
but  will  have  absolutely  no  effect  upon  the  speed.  With  no 
current  in  the  field  winding  the  power  factor  will  be  very  low  and 
the  current  will  lag  far  behind  the  e.m.f.  The  passage  of  a  cur- 
rent through  the  field  will  bring  the  armature  current  more  nearly 
into  phase  with  the  e.m.f.,  and  by  adjusting  the  field  strength  to 
just  the  proper  value,  the  lag  can  be  reduced  to  zero.  A  stronger 
field  current  than  this  will  result  in  a  leading  current.  These 
facts  will  be  more  fully  treated  in  Chap.  XVI. 

168.  Measurement  of  Power  in  Polyphase  Circuits. — The 
construction  of  the  wattmeter  has  been  discussed  in  Chap.  XIII, 
and  its  connection  on  a  single-phase  circuit  is  illustrated  in  Fig. 
105.  It  is  obvious  that  the  total  power  of  a  two-phase  circuit 
can  be  measured  by  connecting  one  wattmeter  in  each  of  the  phases 
as  shown  in  Fig.  127.  The  total  power  will  be  the  sum  of  the 
two  readings.  In  case  two  wattmeters  are  not  available,  it  would  be 
necessary  to  measure  the  power  of  one  phase  and  then  shift  the 
wattmeter  to  the  other  phase.  The  readings  might,  of  course, 
be  far  from  the  truth  if  the  power  should  change  between  the  two 
readings. 

The  connection  shown  in  Fig.  127  will  give  the  total  power 
correctly  only  in  case  the  phases  are  not  interconnected  in  both 
the  load  and  the  generator.  If  the  generator  windings  are  con- 
nected to  one  another  at  their  middle  point  and  the  loads  on  the 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


179 


two  phases  are  similarly  connected,  current  can  flow  out  on  wire 
2  and  back  on  3  without  passing  through  the  current  coils  of  the 
wattmeters  at  all.  Consequently  the  power  developed  by  this 
current  would  not  be  indicated  on  the  instruments.  A  circuit 
of  this  character  would  be  more  properly  called  a  four-phase 


FIG.  127. 

circuit  than  a  two-phase  circuit.     Such  interconnection  on  both 
the  generator  and  the  load  is  not  common. 

169.  Measurement  of  Power  in  Three-phase  Circuits. — If  power 
is  supplied  from  a  star-connected  three-phase  generator  or  from 
three  transformers  connected  in  star,  the  most  obvious  method  of 
measuring  the  power  is  to  employ  three  wattmeters  as  shown  in  Fig. 


FIG.  128. 

128.  The  current  coil  of  each  is  connected  in  one  of  the  line 
wires,  and  all  the  pressure  coils  are  connected  to  the  neutral  point 
at  one  end  and  to  their  respective  line  wires  at  the  other.  Each 
wattmeter  measures  the  power  developed  by  one  of  the  three 
windings,  and  the  sum  of  the  three  readings  will  be  the  total 
power.  Moreover,  if  the  three  phases  are  balanced  the  readings 
of  all  the  wattmeters  will  be  the  same.  This  method  is  not  much 


180      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

used  except  in  laboratory  work,  since  it  requires  the  use  of  three 
wattmeters  and  since  it  is  rarely  the  case  that  the  neutral  point 
is  readily  accessible.  Occasionally  a  small  three-phase  reactor 
is  used  to  provide  an  "  artificial  neutral,"  or  two  non-inductive 
resistors  having  the  same  resistance  as  the  pressure  coil  of  the 
wattmeter  may  be  used  with  it  for  the  same  purpose. 

170.  The  Two-wattmeter  Method.— Referring  to  the  mesh 
connection  of  Fig.  124,  and  the  corresponding  vector  dia- 
gram, Fig.  126,  it  will  be  seen  that  the  sum  of  the  two  e.m.fs., 
A  and  B,  is  equal  to  the  third  e.m.f.  C.  It  is  then  quite  evi- 
dent that  the  third  winding  C  might  be  omitted  and  the  ma- 
chine would  continue  to  operate  as  a  three-phase  gener- 
ator with  only  the  two  windings  as  indicated  in  Fig.  129. 


FIG.  129. 

The  capacity  of  the  machine  would  be  reduced  and  there  would 
be  a  tendency  for  the  voltages  of  the  three  phases  to  differ.  On 
this  account  such  a  winding  is  not  used  on  generators.  Two 
transformers  are,  however,  frequently  so  connected,  since  it  is 
cheaper  to  provide  two  large  transformers  than  three  small  ones. 
It  is  then  evident  that  a  true  three-phase  current  can  be 
obtained  from  two  windings  connected  as  shown  in  Fig.  129. 
It  is  likewise  evident  that  two  wattmeters  connected  as  in  this 
figure  will  measure  correctly  the  total  power  of  the  circuit,  since 
each  of  them  will  measure  the  power  of  its  respective  winding. 
If  the  two  windings  of  Fig.  129  are  replaced  by  three  windings, 
connected  either  in  star  or  in  mesh,  the  currents  in  the  line  wires 
and  the  voltages  between  them  would  not  be  changed,  since  these 
are  determined  by  the  connected  load.  The  power  would  be  the 
same  and  the  readings  of  the  wattmeters  likewise  the  same. 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS  181 

Consequently  the  two  wattmeters  will  measure  correctly  the 
power  of  the  three-phase  circuit. 

Without  going  fully  into  the  reasons,  it  should  be  pointed 
out  that  the  two  wattmeters  will  not  necessarily  read  alike  even 
though  the  circuit  be  balanced.  If  the  circuit  is  balanced  and 
the  power  factor  is  unity,  the  vectors  A,  B,  and  C  in  Fig.  125  may 
be  taken  as  representing  both  the  currents  in  the  three  lines  and 
the  voltages  of  the  three  generator  windings  from  the  neutral 
point  to  the  terminals.  They  are,  however,  not  the  voltages 
between  lines  which  are  represented  both  in  magnitude  and  direc- 
tion by  the  three  vectors  AB,  CA,  and  CB.  If  the  two  currents 
flowing  in  the  two  wattmeter  coils  are  C  and  B,  the  voltages  applied 
across  the  pressure  coils  are  A  B  and  CA.  In  the  one  case  the 
current  lags  30°;  in  the  other  it  leads  by  the  same  angle.  If  the 
circuit  is  balanced  the  two  readings  will  be  the  same. 

Suppose,  however,  that  the  current  lags  30°.  In  the  wattmeter 
in  which  the  current  was  30°  ahead  of  the  e.m.f.,  the  two  will  now 
be  in  phase,  and  in  the  other  instrument  in  which  the  lag  was  30°, 
it  will  now  be  60°.  The  reading  of  the  first  wattmeter  will  now 
be  greater  than  before  while  that  of  the  second  will  be  far  less. 
If  the  lag  of  the  current  in  the  circuit  as  a  whole  becomes  60°,  there 
will  be  a  lag  in  one  meter  of  60°  -  30°  =  30°,  while  in  the  other 
it  will  be  60°  +  30°  =  90°.  The  reading  of  this  second  meter 
will  then  be  zero.  With  still  greater  lag  of  the  current  the  reading 
of  the  second  meter  will  reverse  and  its  indication  must  then  be 
subtracted  from  that  of  the  first.  It  should  also  be  noted  that  a 
lag  of  60°  corresponds  to  a  power  factor  of  0.5,  and  this  is  then  the 
power  factor  of  the  circuit,  when  the  reading  of  one  meter  is  zero. 

The  two-wattmeter  method  as  described  is  correct  for  unbal- 
anced loads,  for  any  power  factor  and  for  distorted  waves  of 
current  or  e.m.f. 

171.  Polyphase  Wattmeters. — In  many  cases  it  is  a  great 
convenience  as  well  as  an  aid  to  accuracy  to  be  able  to  determine 
the  power  in  a  polyphase  circuit  with  one  reading.  This  is 
particularly  true  in  the  case  of  switchboard  instruments.  An 
instrument  to  do  this  can  be  readily  constructed  by  mounting 
two  wattmeter  movements  on  one  spindle.  The  torques  of  the 
two  will  then  be  automatically  added  or  subtracted  as  the  case 
may  require,  and  the  total  indication  of  the  instrument  will  be 
proportional  to  the  total  power  of  the  circuit.  The  same  prin- 
ciple may  be  applied  to  watthour  meters.  Polyphase  meters 


182      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

may  be  operated  on  single-phase  circuits  by  connecting  in  only 
one  side  of  the  meter,  or  both  sets  of  coils  may  be  connected  in 
series  or  in  parallel. 

172.  Power  Factor   of  Unbalanced    Polyphase  Circuits. — In 
a  two-  or  three-phase  circuit  the  voltages,  currents  and  power  fac- 
tors may  all  be  different.     There  are  then  two  or  three  different 
power  factors  so  that  the  term  power  factor  as  applied  to  the 
whole  circuit  loses  its  significance.     It  is  the  common  practice 
when  the  unbalancing  is  not  too  great  to  take  the  average  current 
and  the  average  voltage,  and  compute  the  power  factor  as  though 
the  circuit  were  balanced.    This  will  give  results  good  enough  for 
ordinary  commercial  purposes.     However,  it  is  not  at  all  impos- 
sible with  this  method  to  obtain  power   factors  greater  than 
unity,  a  result  obviously  absurd. 

173.  Line  Regulation. — Every  transmission  line  has  resistance, 
inductance  and  capacitance.     The  last  is  due  to  the  fact  that  the 
two  wires  comprising  a  line  are  at  different  potentials  and  are 
separated  by  an  insulator;  namely,  the  air,  or  in  the  case  of  a 
cable,  whatever  insulating  material  is  used.     Since  the  conductors 
are  quite  a  distance  apart  (except  in  the  case  of  cables)  the  con- 
denser effect  is  small  unless  the  line  is  very  long  or  the  voltage 
high.     In  the  following  discussion  it  will  be  neglected. 

Both  the  capacitance  and  the  inductance  of  a  line  are  distributed 
along  the  line,  whereas  in  ordinary  computations  it  is  assumed 
that  they  are  "lumped"  at  one  or  more  points.  If  all  of  these 
factors  are  taken  into  account,  the  problem  of  line  regulation  be- 
comes very  complicated.  In  the  following  discussion  it  is  assumed 
that  the  capacitance  may  be  entirely  neglected  and  that  the  in- 
ductance is  "  lumped  "  at  one  point  of  the  line.  The  results  will  be 
commercially  correct  for  short  lines  operating  at  moderate  voltages. 

174.  Regulation  at  100  Per  Cent.  Power  Factor.— Fig.   130 
shows  the  vector  diagram  of  a  transmission  line  when  the  con- 
nected load  is  non-inductive.     E  represents  the  voltage  at  the 
receiving  end  of  the  line,  and  /,  the  current  in  phase  with  it. 
To  the  terminal  voltage  must  be  added  a  voltage  RI  to  overcome 
the  ohmic  drop  in  the  line  and  a  voltage,  L/co,  to  overcome  the 
inductive  drop.     The  first  is  in  phase  with  the  line  current  and 
the  latter  90°  ahead  of  it.     The  voltage  which  must  be  applied  to 
the  sending  end  of  the  line  is  represented  by  E0.     It  will  be  seen 
that  the  applied  voltage  is  larger  than  the  voltage  at  the  receiv- 
ing end  and  is  somewhat  ahead  of  it  in  phase. 


SINGLE-PHASE  AND  POLYPHASE  SYSTEMS 


183 


175.  Regulation  with  Lagging  Current. — The  vector  diagram 
for  lagging  current  is  shown  in  Fig.  131.  The  same  principles 
are  applied.  It  will  be  apparent  that  if  E  is  the  same  as  in  the 


Liu 


Liu 


FIG.  130. 

first  case  the  applied  voltage  must  be  much  greater,  or  the  drop  is 
far  greater. 

176.  Regulation  with  Leading  Current. — Fig.  132  shows  the 
method  of  finding  the  regulation  when  the  current  is  leading. 
If  the  RI  drop  is  small  and  the  L/OJ  drop  large,  it  will  be  evident 
that  E0  may  be  smaller  than  E,  that  is,  the  voltage  is  greater  at 
the  receiving  end  than  at  the  sending  end.  It  should  not  be 
inferred  that  the  power  is  greater  at  the  re- 
ceiving end.  This  would  be  impossible,  and 
it  will  always  be  found  that  the  product  of  E0 
and  /  times  the  cosine  of  the  angle  between 
them  is  greater  than  El  times  the  cosine  of 
the  angle  between  them. 

It  will  be  clear  now  that  the  regulation  of 
a  line  depends  not  only  upon  the  constants  of 
the  line  itself,  but  also  upon  the  kind  of  load 
that  is  supplied  from  it.  If  the  load  consists 
of  incandescent  lamps  with  a  power  factor  of 
nearly  100  per  cent,  the  drop  will  be  small  and  the  regulation 
good.  If  the  line  supplies  a  load  of  induction  motors  taking  a 
lagging  current,  the  regulation  will  be  much  poorer.  If  on  the 
other  hand  the  load  consists  of  an  over-excited  synchronous 
motor  or  other  load  capable  of  taking  a  leading  current  the  volt- 
age at  the  far  end  of  the  line  may  be  greater  than  the  sending 
voltage,  or  the  regulation  may  be  negative.  The  power  loss  in 
the  line  will  be  the  same  in  all  cases  for  the  same  current.  For 
the  same  power  the  current,  and  therefore  the  loss,  will  be  least 
if  the  power  factor  is  100  per  cent. 

The  above  method  can  be  applied  to  each  phase  of  a  two-phase 
circuit.     In  the  case  of  a  three-phase  line  E0  and  E  should  be 


Liu    . 


RI 
FIG.  132. 


184      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

taken  as  the  voltages  from  the  neutral  point  to  the  line  and  the 
same  method  applied. 

PROBLEMS 

74.  An  alternator  has  ten  poles  and  revolves  at  a  speed  of  720  r.p.m. 
What  is  the  frequency? 

75.  At  what  speed  must  a  two-pole  alternator  revolve  in  order  that  the 
frequency  may  be  60  cycles  per  second?     What  is  the  highest  possible 
speed  of  a  60-cycle  alternator?     Of  a  25-cycle  alternator? 

76.  In  the  case  of  a  three-phase  star-connected  armature  the  voltage  from 
the  neutral  point  to  each  terminal  was  1328  volts,  the  current  per  line  wire 
was  100  amp.,  and  the  receiving  circuit  was  non-inductive,  so  that  the  lag 
was  zero.     What  was  the  voltage  between  line  wires?     What  was  the  power 
output  of  the  generator? 

77.  In  measuring  the  power  output  of  a  three-phase  generator,  three 
wattmeters  were  connected  as  shown  in  Fig.  128.     The  reading  of  each  was 
1000  watts,  the  voltage  between  line  wires  was  230  volts,  and  the  current  in 
each  line  wire  was  12  amp.     What  was  the  power  factor? 

78.  Two  wattmeters  connected  as  shown  in  Fig.  129  to  a  three-phase 
alternator  gave  readings  of  2000  watts  and  1200  watts  respectively.     The 
current  in  each  line  was  7  amp.  and  the  line  voltage  was  440.     What  was  the 
power  output?      What  was  the  power  factor? 

79.  A  single-phase  transmission  line  20  miles  long  and  operating  at  60 
cycles  consists  of  two  No.  6  conductors  having  a  resistance  of  0.395  ohm 
per  1000  ft.  of  each  wire  or  a  resistance  of  0.79  ohm  per  1000  ft.  of  line. 
The  inductance  is  0.0077  henry  per  1000  ft.  of  line.     The  voltage  at  the  end 
of  the  line  is  22,000  and  the  current  is  10  amp.  at  unity  power  factor. 
What  is  the  power  at  the  end  of  the  line?     What  is  the  power  loss  in  the 
line?     What  is  the  power  at  the  beginning  of  the  line?     What  is  the  effi- 
ciency of  the  line? 

80.  In  the  above  line  what  is  the  resistance  drop  ?     What  is  the  drop  due 
to  reactance?     Draw  the  vector  diagram  and  determine  the  voltage  at  the 
beginning  of  the  line.     What  is  the  power  factor  at  the  beginning  of  the  line? 

81.  Solve  the  preceding  problem  for  a  power  factor  of  0.6  lagging  current 
at  the  end  of  the  line. 

82.  Solve  the  preceding  problem  for  a  power  factor  of  0.6  leading  current 
at  the  end  of  the  line. 

83.  In  testing  a  certain  single-phase  transmission  line  the  far  end  of  the 
line   was    short-circuited   and   60-cycle  current  was  then   passed  through 
the  line.     Readings  were  taken  as  follows:    Amperes  50,  volts  106,  watts 
2700.     What  was  the  resistance  of  the  line?     What  was  the  reactance? 
The  impedance?     The  inductance? 

84.  In  the  above  line  the  power  at  the  end  was  100  kw.     The  voltage  was 
2200,  the  current  45.5  amp.     What  was  the  efficiency  of  the  line? 

85.  In  the  above  line,  what  was  the  voltage  at  the  beginning  of  the  line? 
What  was  the  regulation  on  unity  power  factor? 

86.  In  the  foregoing,  assuming  that  the  current  and  voltage  were  the  same 
at  the  end  of  the  line,  but  that  the  power  was  zero,  what  was  the  voltage  at 
the  beginning  of  the  line?     What  was  the  regulation? 


CHAPTER  XV 
THE  TRANSFORMER 

177.  Transformation  of  Continuous  Current. — To  transform 
a  continuous  current  from  one  voltage  to  another,  is  a  difficult 
and  expensive  process.     For  example,  a  current  of  100  amp.  at 
1000  volts,  corresponding  to  100  kw.  might  be  converted  to  a 
current  of  nearly  1000  amp.  at  100  volts.     The  power  would 
again  be  nearly  100  kw.,  the  difference  being  due  to  the  power 
lost  in  the  transformation.     To  carry  out  this  transformation, 
the  simplest  process  would  be  to  employ  a  direct-current  motor 
operating  at  1000  volts,  and  driving  a  direct- current  generator 
furnishing  current  at  100  volts.     This  would  necessitate  the  use 
of  machinery,  of  a  total  capacity  of  200  kw.     The  machinery 
would  be  expensive  since  it  contains  rotating  parts,  and  would 
cost  say  $4000.     It  would  require  the  constant  presence  of  an 
attendant  and  the  process  would  moreover  be  rather  inefficient. 
The  loss  in  the  case  cited  would  be  about  20  kw.,  giving  an  effi- 
ciency of  80  per  cent.     For  these  reasons,  continuous  currents  are 
rarely  transformed  in  voltage. 

On  the  other  hand,  alternating  current  can  be  readily 
transformed  from  one  voltage  to  another.  The  cost  of  a  suitable 
transformer  for  the  conditions  described  would  be  about  $500. 
Its  efficiency  would  be  say  98  per  cent.  Since  it  has  no  moving 
parts,  the  only  attention  required  would  be  inspection  at  infre- 
quent intervals.  Such  transformers  are  therefore  used  freely 
in  alternating-current  practice. 

178.  General  Construction  of  Transformer. — A  view  of  the 
exterior  of  a  lighting  transformer  is  shown  in  Fig.  133,  and  the 
interior  of  the  same  transformer  is  shown  in  Fig.  134.     Essentially 
the  transformer  consists  of  a  core  of  laminated  iron  forming  a 
closed   magnetic  circuit,  and  usually  two  coils  of  wire   wound 
around  this  magnetic  circuit.     This  is  illustrated  in  Fig.    135. 
In  practice,  the  coils  are  not  wound  on  opposite  sides  of  the  rec- 
tangle as  shown,  but  in  general,  each  coil  is  divided  and  one-half 
is  wound  on  one  side  and  half  on  the  other.     Thus  the  coils  are 

185 


186      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


wound  one  on  top  of  the  other,  and  the  opportunity  for  magnetic 
leakage  is  decreased. 


FIG.  133. 

179.  Elementary   Theory. — Consider   now   that   there   is   an 
harmonically  varying  flux  in  the  laminated  iron  core  of  Fig.  135. 


FIG.  134. 

For  the  present  this  flux  may  be  considered  as  produced  in  any 
convenient  manner,  say  by  means  of  an  alternating  current  in  a 
third  coil  on  the  core.  This  flux  will  induce  a  certain  e.m.f.  in 


THE  TRANSFORMER 


187 


100  V. 
100  Amp. 

\\\\\ 

1000  V. 
10  Amp. 

FIG.  135. 


each  turn  of  both  the  secondary  and  the  primary,  and  this  e.m.f. 
will  be  the  same  per  turn  in  each,  provided  there  is  no  magnetic 
leakage,  that  is,  if  all  of  the  flux  which  passes  through  one  of  the 
coils  passes  through  the  other  also.     The  total  e.m.f.  induced  in 
either  of  the  coils  will  be  the  e.m.f. 
per  turn,  multiplied  by  the  number 
of  turns  in  the  coil.     This  gives  at 
once  the  first  important  law  of  the 
transformer,  namely,  that  the  e.m.fs. 
induced  in  the  primary  and  secondary 
are    proportional   to   the  number  of 
turns    in    the    respective    windings. 
Moreover  the  induced  e.m.fs.  will  be 
in  the  same  direction  around  the  core. 
In  practice,  the  magnetic   flux  of 
the  transformer  is   supplied   not   by 
means   of   a   third   winding,    but   by 
means  of  a  current  circulating  in  one 
of  the  two  main  windings.    This  wind- 
ing is  called   the  primary.     If  no  current  is   taken   from   the 
secondary,  the  current  which  will  flow  in  the  primary  when  it 
is  connected  across  the  mains  will  be  very  small  compared  to  the 

full-load  current  of  the  transformer. 
This  arises  from  the  fact  that  few 
ampere  turns  are  required  to  mag- 
netize the  core,  since  it  is  a  closed 
magnetic  circuit,  and  is  built  of  iron 
with  a  low  magnetic  reluctance.  In 
general,  about  2  per  cent,  of  the  full- 
load  current  is  required  to  magnetize 
the  core. 

180.  Core  Loss.- — While  operating 
in  this  manner  on  open  circuit,  there 
is  a  loss  in  the  transformer  called  the 
core  loss.  This  loss  is  composed  of 
two  parts,  that  due  to  eddy  currents 
and  that  due  to  hysteresis.  The 
former  is  caused  by  currents  circulating  in  the  iron  of  the  core. 
From  a  cross-section  of  a  few  laminations  as  shown  in  Fig.  136 
it  will  be  apparent  that  if  the  flux  is  in  a  direction  perpendicu- 
lar to  the  paper,  there  is  an  opportunity  for  currents  to  cir- 


FIG.  136. 


188      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

culate  in  the  core  as  shown.  The  section  of  a  lamination  will 
have  induced  in  it  an  e.m.f.  just  as  though  it  were  a  turn  of 
wire  of  the  same  dimensions.  This  e.m.f.,  it  is  true,  is  small, 
since  only  a  small  amount  of  flux  passes  through  any  one  lami- 
nation, but  on  the  other  hand,  the  resistance  is  small  also,  and 
consequently  a  considerable  current  may  be  set  up.  This  cur- 
rent may,  however,  be  reduced  to  as  small  an  amount  as  neces- 
sary by  decreasing  the  thickness  of  the  laminations.  The  sheets 
are  therefore  made  as  thin  as  considerations  of  economy  in  con- 
struction will  allow. 

The  exact  cause  of  hysteresis  loss  is  not  known.  It  is  supposed, 
however,  that  when  a  piece  of  iron  is  magnetized,  the  molecules 
of  the  iron  turn  somewhat  upon  their  axes,  so  as  to  point  along 
the  lines  of  the  magnetic  induction.  When  the  magnetism  is 

reversed,  the  molecules  turn  more 
/^  or  less  so  as  to  point  in  the  oppo- 

site direction.     In  turning  in  this 
I— Applied  E  M  F        manner,    there   is   apparently    de- 
veloped an  internal  friction,  anal- 


Power 
Component 
of  Current 


/    xNo  Load  Current 


,1  .•       ->          -i 

ogous    to    that    noticed    when    a 

piece  of  steel  is  bent  rapidly  back- 
Magnetizing  Current  ,    .  i       m  •     1 

induced  E  M  F1  ward  and  forward.     This  loss  in- 

creases in  direct  proportion  to  the 
number   of   reversals   per   second, 
FIG.  137.  and  also  increases  with  the  mag- 

netic density,  although  not  in  direct 

proportion  to  it.  The  core  loss  will  be  from  as  high  as  4  per 
cent,  of  full-load  capacity  in  small  transformers,  to  as  low  as 
0.5  per  cent,  in  large  ones. 

181.  Vector  Diagram  of  Unloaded  Transformer.  —  It  is  now 
possible  to  draw  the  vector  diagram  of  an  unloaded  transformer. 
The  start  is  made  with  the  magnetizing  current  (see  Fig.  137). 
In  the  diagram  this  is  drawn  as  a  horizontal  line.  It  might,  of 
course,  have  been  drawn  in  any  direction,  since  the  diagram  as 
a  whole  is  supposed  to  be  rotating  around  the  center  point  once 
for  each  cycle  of  the  current.  The  magnetism  is  assumed  for 
the  present  to  be  proportional  at  each  instant  to  the  magnetizing 
current.  This  would  be  strictly  true  if  the  core  were  composed 
of  air  instead  of  iron.  With  an  iron  core,  on  account  of  the  satu- 
ration of  the  iron,  and  the  core  loss,  this  is  not  strictly  true,  but 
it  is  near  enough  for  the  present  purpose. 


THE  TRANSFORMER  189 

The  variation  of  flux  may  be  represented  by  an  equation  of 
the  form 

(f>  =  $  sin  cot 

At  any  instant,  the  induced  e.m.f  .  will  be  equal  to  —  AT  —  where 

N  is  the  number  of  turns  on  the  primary,  or  performing  the  differ- 
entiation, 

—  6   =  N  -77    =   $Nu  COS  0)t 

dt 

From  this  it  appears  that  the  induced  e.m.f.  has  a  maximum 
value  equal  to 


or  changing  to  effective  values,  by  dividing  by  \/2>  and  dividing 
by  108  to  reduce  to  volts, 

E  =  4.44/JV$  -f-  108 

From  the  equation,  it  is  seen  that  the  induced  e.m.f.  is  90°  be- 
hind the  flux  and  consequently  also  90°  behind  the  magnetizing 
current.  It  will  therefore  be  represented  by  a  vector  drawn  as 
shown  in  the  diagram.  The  e.m.f.  which  must  be  applied  to  over- 
come this  induced  e.m.f.  will  be  represented  by  an  exactly  equal 
and  opposite  vector. 

Considering  the  diagram  as  explained  so  far,  it  will  be  noted 
that  the  current,  and  the  applied  e.m.f.  are  at  right  angles,  and 
therefore  the  power  is  zero.  As  stated,  however,  there  is  a  core 
loss  in  the  transformer.  To  supply  this  loss,  it  is  necessary  to 
have  a  component  of  the  current  in  phase  with  the  applied  e.m.f. 
This  component  will  therefore  be  represented  by  a  vertical  line 
as  shown.  The  total  current  will  be  the  resultant  of  these  two 
currents,  and  is  called  the  no-load  current  or  the  leakage  current. 

Perhaps  the  explanation  of  the  foregoing  phenomenon  would 
have  been  more  simple  though  not  so  complete  if  we  had  started 
with  the  no-load  current,  and  explained  that  on  account  of  the 
magnetic  friction  or  hysteresis,  the  magnetism  will  lag  behind 
the  current  by  a  small  angle  as  shown. 

In  addition  to  the  above,  a  small  e.m.f  will  be  required  to 
overcome  the  resistance  of  the  primary  coil.  As  noted  before, 
the  no-load  current  is  very  small,  and  consequently  the  drop 
due  to  it  is  entirely  negligible.  For  completeness  it  may,  how- 
ever, be  represented  by  means  of  a  short  vector  drawn  parallel 


190      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

to  the  vector  representing  the  current.  The  applied  e.m.f.  will 
then  be  a  vector  equal  to  the  sum  of  the  e.m.f.  required  to  over- 
come the  self-induced  e.m.f.  and  the  e.m.f.  required  to  force  the 
current  through  the  resistance  of  the  primary.  In  the  figure 
the  latter  vector  is  shown  much  exaggerated. 

In  all  of  the  foregoing  discussion,  the  secondary  coil  has  been 
assumed  to  be  on  open  circuit.  There  has  therefore  been  no 
current  in  it,  and  it  has  been  entirely  without  effect.  All  of  the 
explanation  will  therefore  apply  to  the  case  of  a  single  coil  wound 
on  an  iron  core.  In  this  case,  the  apparatus  would  be  called  a 
choke  coil,  or  simply  an  inductor.  If  no  iron  had  been  present, 
the  diagram  would  have  been  modified  by  the  fact  that  the  no- 
load  current  would  be  identical  with  the  magnetizing  current. 

182.  Transformers  under  Load. — As  soon  as  a  current-con- 
suming apparatus  is  connected  to  the  secondary  of  a  transformer, 
the  conditions  change.  The  first  point  to  be  noted  is  that  the 
flux  through  the  core  remains  approximately  constant.  This 
follows  from  the  fact  that  the  induced  e.m.f.  in  the  primary  of 
the  transformer  is  at  all  times  nearly  equal  to  the  applied  e.m.f. 
Since  this  induced  e.m.f.  is  constant,  the  flux  which  produces 
it  will  be  constant  also.  Likewise  the  core  loss,  being  dependent 
upon  the  magnetic  flux,  will  be  constant  irrespective  of  the  load. 
It  is' therefore  proper  to  consider  the  line  marked  "  no-load  cur- 
rent" as  being  constant. 

In  considering  the  loaded  transformer,  it  will  be  simpler  to 
assume  a  transformer  with  a  one  to  one  ratio,  that  is,  with  the 
same  number  of  turns  in  the  secondary  as  in  the  primary.  Any 
deductions  made  by  considering  such  a  transformer  will  apply 
equally  well  to  a  transformer  of  a  different  ratio.  With  this 
understanding,  the  e.m.f.  induced  in  the  secondary  will  be  repre- 
sented by  the  same  line  as  that  showing  the  induced  voltage  in 
the  primary. 

When  current  is  taken  from  the  secondary,  the  angular  rela- 
tion of  the  current  to  the  e.m.f.  will  be  dependent  upon  the 
nature  of  the  receiving  circuit.  If  this  circuit  contains  resistance 
and  inductance,  the  current  will  lag.  On  the  other  hand,  if 
capacitance  is  present,  the  current  may  be  ahead  of  the  e.m.f.  In 
Fig.  138  it  is  assumed  that  the  former  is  the  case,  and  the  current 
has  been  drawn  lagging  behind  the  induced  e.m.f.  by  an  angle  B8. 
The  magnetizing  force,  acting  upon  the  core  of  the  transformer, 
is  the  resultant  of  all  of  the  currents  acting.  As  soon  as  current 


THE  TRANSFORMER 


191 


passes  in  the  secondary,  it  as  well  as  the  primary  current  will 
tend  to  magnetize  the  core.  In  fact,  in  most  cases,  the  secondary 
current  will  be  far  stronger  than  the  no-load  current  in  the  pri- 
mary. From  the  direction  in  which-it  is  drawn,  it  will  be  apparent 
that  the  secondary  alone  would  tend  to  exert  a  strong  demag- 


Angle  of  Lag_ 

of  Current      -^ 

-/   i 

Primary  Current 

y^-i — »     E.M.F. 

/ /  ^   -T, 


Secondary 
Current 


/ 


Secondary 
^Induced  E.M.F. 


FlG.    138. 


FIG.  139. 


netizing  effect  upon  the  core.  As  soon  as  this  takes  place,  the 
back  induced  e.m.f.  of  the  primary  will  be  reduced  and  the  ap- 
paratus will  take  more  current  from  the  main  through  the  pri- 
mary. The  value  of  this  additional  current  will  be  just  enough. 
to  offset  the  demagnetizing  effect  of  the  current  in  the  secondary 
The  resultant  of  the  primary  and  the  sec- 
ondary current  will  then  be  just  equal  to 
the  required  no-load  current.  The  con- 
struction of  the  parallelogram,  giving  the 
resultant  of  these  two  currents  is  shown 
in  Fig.  138. 

Figure  139  illustrates  a  case  in  which 
the  current  instead  of  lagging,  is  in  phase 
with  the  secondary  e.m.f.  The  primary 
current  lags  somewhat  behind  the  primary 
e.m.f.,  or  in  other  words,  the  primary  and 
the  secondary  currents  do  not  differ  by 
exactly  180°.  In  Fig.  140  is  shown  a  case 

where  the  current  in  the  secondary  is  leading.  The  primary 
current  in  this  event  usually  leads  also,  although  it  might  happen 
that  it  would  not  if  the  secondary  lead  were  small.  The  no-load 
current  in  all  of  these  diagrams  is  exaggerated  so  that  the  devia- 
tion of  the  primary  and  secondary  currents  from  exact  opposition 


pJG< 


192      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

is  also  exaggerated.  In  practice,  the  primary  and  secondary 
currents  are  nearly  in  opposition.  In  fact,  transformers  are 
frequently  used  to  transform  to  a  smaller  current  when  a  large 
alternating  current  is  to  be  measured  by  means  of  an  ammeter 
or  wattmeter,  capable  of  carrying  only  a  small  current.  Unless 
such  measurements  are  to  be  very  exact,  it  is  usually  assumed 
that  the  primary  and  secondary  currents  are  in  the  inverse  ratio 
of  the  turns,  and  that  they  are  in  exact  phase  opposition. 

183.  Leakage  Flux. — When  a  transformer  is  under  load,  the 
greater  part  of  the  magnetic  flux  passes  through  both  the  primary 
and  the  secondary  coils.  It  will  be  seen,  however  that  there  is 
an  opportunity  for  some  flux  to  surround  one  of  the  coils  without 
passing  through  the  other.  In  practice,  every  effort  is  made  to 
reduce  the  amount  of  this  leakage  flux,  but  some  is  always  present. 


Lplpu 


FIG.  142. 


The  main  flux  is  nearly  in  phase  with  the  resultant  of  the 
primary  and  the  secondary  currents.  The  leakage  fluxes  on  the 
other  hand,  pass  through  only  one  of  the  two  coils.  They  are 
therefore  nearly  in  phase  with  the  currents  in  their  respective 
coils.  Each  of  these  fluxes  therefore  induces  an  e.m.f.  in  its 
respective  coil,  lagging  nearly  90°  behind  the  current  in  the  coil. 
In  the  case  of  the  secondary,  this  e.m.f.  is  added  vectorially  to 
the  terminal  e.m.f.  In  the  primary,  an  additional  e.m.f.  equal 
and  opposite  to  this  induced  e.m.f.  must  be  added  vectorially  to 
overcome  it.  In  addition  to  this,  it  is  necessary  to  add  vectorially 
to  the  primary  the  e.m.f.  required  to  overcome  the  resistance  of 
the  primary  winding,  and  to  subtract  a  similar  quantity  from  the 
secondary  voltage.  These  latter  two  vectors  will  be  in  phase 
with  the  respective  currents.  The  complete  construction  of  the 


THE  TRANSFORMER  193 

vector  diagram  for  the  case  of  a  lagging  current  is  shown  in  Fig. 
141,  and  Fig.  142  shows  the  same  for  a  leading  current.  In  the 
former  case,  the  voltage  at  the  secondary  terminals  is  less  than 
that  at  the  primary  terminals,  while  with  the  leading  current, 
the  secondary  voltage  is  greater  than  that  of  the  primary.  Stated 
generally,  it  may  be  said  that  the  secondary  voltage  may  be 
either  somewhat  less  or  somewhat  more  than  would  be  indicated 
by  the  ratio  of  the  number  of  turns  on  the  primary  and  on  the 
secondary. 

184.  Regulation. — The    foregoing    discussion    introduces    the 
subject  of  transformer  regulation.     Good  regulation  in  a  trans- 
former means  that  the  secondary  voltage  varies  but  little  as  the 
load  is   changed,  the  primary  voltage  being  constant.     Good 
regulation  is  highly  desirable,   particularly  when  transformers 
are  used  for  house  to  house  distribution.     The  attempt  is  made 
at  the  central  station  to  keep  the  primary  voltage  as  nearly  con- 
stant as  possible.     The  inherent  regulation  of  the  transformers 
is  relied  upon  to  keep  the  secondary  voltage  also  constant. 

Technically,  the  regulation  is  defined  as  the  rise  in  voltage  of 
the  secondary  when  full  load  is  thrown  off  the  transformer, 
divided  by  the  full-load  voltage,  the  frequency  and  primary 
voltage  remaining  constant.  The  foregoing  will  show  that  this 
regulation  will  be  dependent  upon  the  nature  of  the  load  carried. 
If  the  current  is  leading,  the  regulation  may  even  be  negative. 
The  term  regulation  is  therefore  meaningless,  unless  the  condi- 
tions are  known.  Ordinarily,  the  regulation  at  unity  power 
factor  is  the  important  one,  particularly  for  lighting  transformers. 
Unless  otherwise  specified,  this  would  be  understood. 

If  transformers  are  to  be  used  to  supply  current  to  induction 
motors,  the  current  will  always  be  lagging.  Under  these  circum- 
stances, there  is  a  strong  argument  in  favor  of  specifying  the 
regulation  at  zero  power  factor  with  lagging  current.  The  advan- 
tage of  this  is  that  the  regulation  is  specified  for  the  worst  possible 
condition,  and  in  practice  better  results  than  this  can  be  counted 
upon. 

185.  Constant-current  Transformers. — In  continuous-current 
practice,  the  constant-current  system  of  distribution  is  nearly 
obsolete.     For  street  lighting  by  means  of  alternating  current, 
using  either  arc  lamps  or  incandescent  lamps,  it  has  however 
great  advantages.     Because  such  circuits  are  out  of  doors,  the 
allowable  voltage  is  much  higher  than  for  interior  illumination. 

13 


194      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

By  operating  the  lamps  in  series,  the  current  to  be  carried  is 
much  reduced,  and  the  investment  in  copper  correspondingly 
reduced.  Such  high  voltage  circuits  are  not  allowed  inside  of 
buildings  on  account  of  the  insurance  regulations,  but  are  in  al- 
most universal  use  for  outside  work. 

A  special  transformer  is  required  to  transform  from  constant 
potential  at  which  the  current  is  generated  to  constant  current. 


FIG.  143. 

A  transformer  for  this  purpose  is  shown  in  Fig.  143.  It  has  two 
coils,  one  of  which  is  free  to  move  away  from  or  toward  the  other. 
The  weight  of  the  moving  coil  is  partially  counterbalanced  by  the 
weights  shown.  When  the  machine  is  in  operation,  there  is  a 
repulsion  between  the  two  coils,  because  the  currents  are  in 
opposite  directions  in  the  two.  This  repulsion  together  with  the 


THE  TRANSFORMER  195 

weights  used,  is  enough  to  hold  the  moving  coil  suspended  in  the 
proper  position.  If  for  any  reason  the  current  increases,  the 
repulsion  of  the  two  coils  increases  and  the  coils  are  forced  further 
apart.  This  in  turn  results  in  an  increased  magnetic  leakage. 
Less  of  the  useful  flux  of  the  transformer,  therefore,  passes 
through  the  secondary,  and  at  the  same  time  the  leakage  flux 
is  increased  in  both  primary  and  secondary.  The  reduction  of 
the  useful  flux  results  in  a  reduction  of  the  secondary  voltage, 
and  consequently  the  current  is  reduced.  By  properly  shap- 
ing the  curves  of  the  arms,  the  current  may  be  made  to 
remain  the  same  whatever  the  position  of  the  moving  coil.  The 
whole  transformer  is  usually  immersed  in  oil  on  account  of  the 
better  cooling  and  the  improved  insulation. 

With  some  types  of  arc  lamps,  a  direct  current  is  preferable  or 
necessary,  or  it  may  be  that  the  constant-current  transformer  is 
to  be  used  to  feed  a  circuit  formerly  supplied  by  a  direct-current 
machine.  In  this  event,  it  is  customary  to  rectify  the  secondary 
current  by  means  of  a  mercury  arc  rectifier.  These  have  a  very 
high  efficiency  at  the  high  voltage  used.  They  are  commonly 
completely  immersed  in  oil  to  secure  better  insulation  and  cool- 
ing. (See  Art.  244.) 

186.  Instrument  Transformers. — Transformers  are  frequently 
used  in  connection  with  measuring  instruments.  For  pressures 
up  to  about  600  volts,  voltmeters  adapted  to  be  directly  connected 
across  the  line  are  commonly  used.  For  voltages  of  1100  or  more 
this  becomes  rather  impracticable,  since  a  large  resistance  would 
be  required  for  such  a  voltmeter.  Moreover  it  is  undesirable 
to  have  a  voltage  of  this  or  greater  magnitude  present  on  the 
front  of  a  switchboard  on  account  of  the  danger  to  life.  The 
difficulty  is  readily  met  by  using  a  small  transformer  to  reduce  the 
voltage  to  a  value  usually  near  100  volts.  The  scale  of  the  instru- 
ment may  be  calibrated  to  read  directly  the  line  pressure  instead 
of  the  secondary  pressure. 

For  similar  reasons  current  transformers  are  frequently  used. 
The  current  to  be  measured  may  be  so  great  that  it  would  be 
impracticable  to  construct  an  instrument  capable  of  carrying  it, 
or  the  voltage  may  be  so  high  that  it  is  desirable  to  have  the 
ammeter  insulated  from  the  Ikie.  Transformers  for  this  pur- 
pose are  usually  wound  to  have  a  full-load  secondary  current 
of  5  amp.  The  scale  may  as  before  be  calibrated  to  read  the 
primary  current  directly. 


196      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


In  using  the  pressure  transformer  little  error  is  introduced. 
Moreover,  practically  all  alternating-current  systems  are  operated 
at  constant  potential,  and  the  voltmeters  are  required  to  read 
only  one  value  of  the  voltage  with  accuracy.  Any  possible  error 
at  this  one  point  may  be  completely  corrected  for  by  calibrating 
the  voltmeter  and  transformer  as  a  unit. 

An  ammeter  is  required  to  operate  over  a  larger  range,  and  the 
error  in  a  current  transformer  is  likely  to  be  larger  than  in  the 
case  of  the  pressure  transformer.  The  error  may  be  corrected 
for  as  before  by  calibrating  the  transformer  and  ammeter  as  a 
unit.  It  is,  however,  rarely  necessary  to  do  this. 


FIG.  144. 

The  only  measuring  instruments  whose  accuracy  is  at  all  seri- 
ously affected  by  the  use  of  instrument  transformers,  are  watt- 
meters and  watthour  meters.  These  are  frequently  used  in  con- 
nection with  both  potential  and  current  transformers.  Unfor- 
tunately, in  addition  to  the  ratio  error  just  mentioned,  both  of 
these  types  of  transformers  introduce  a  small  phase  error.  This 
becomes  of  some  moment,  especially  if  the  power  factor  of  the 
load  to  be  measured  is  low.  The  indications  of  wattmeters  pro- 
vided with  either  potential  or  current  transformers  should  there- 


THE  TRANSFORMER 


197 


fore  be  accepted  with  some  caution,  particularly  if  the  load  is 
small  and  the  power  factor  low. 

187.  Types  of  Transformers. — Three  general  types  of  trans- 
formers are  in  use,  the  core  type,  the  shell  type,  and  a  com- 
bination of  the  two  preceding  called  the  cruciform  type.  The 
core  type  has  been  described  and  is  illustrated  in  Figs.  133  and  134. 
If  the  coils  and  the  core  in  the  core  type  of  transformer  are  inter- 


FIG.  145. 

changed  the  shell  type  illustrated  in  Fig.  144  is  obtained.  It 
may  be  considered  that  the  core  type  has  one  core  and  two  coils, 
while  the  shell  type  has  two  cores  and  one  coil.  The  flux  after 
passing  through  the  coils  divides  into  two  parts  and  returns  on 
the  outside. 

The  cruciform  type  of  transformer,  shown  in  Fig.  145,  is  a  modi- 
fication of  the  shell  type.     The  return  magnetic  circuit,  instead 


198      PRINCIPLED  OF  DYNAMO  ELECTRIC  MACHINERY 


of  being  divided  into  two  parts,  consists  of  four  separate  limbs. 
This  possesses  the  advantage  over  the  shell  type  that  the  amount 
of  iron  required  is  not  so  great.  This  is  apparent  since  the  aver- 
age distance  to  be  traveled  by  the  returning  lines  of  induction  is 
slightly  less. 

188.  Cooling  of  Transformers. — The  cooling  of  small  trans- 
formers presents  no  particular  difficulty.  The  core  and  coils 
are  practically  always  enclosed  in  an  iron  case  filled  with  insu- 
lating  oil.  The  oil,  in  addi- 
tion to  its  insulating  proper- 
ties, insures  that  all  parts  of 
the  transformer  remain  at 
practically  the  same  tem- 
perature. If  any  point  be- 
comes hotter  than  the  aver- 
age, the  oil  in  its  vicinity 
becomes  heated  and  rises. 
Its  place  is  taken  by  cooler 
oil,  and  thus  there  is  a  ten- 
dency to  equalize  the  tem- 
perature. 

As  transformers  increase 
in  size,  the  problem  of  dis- 
posing of  the  heat  becomes 
more  serious.  The  losses  of 
a  transformer  may  be  as- 
sumed to  be  approximately 
proportional  to  the  volume 
or  weight  of  the  apparatus. 
This  will  be  the  case  if  the 

current  densities  and  the  magnetic  densities  are  the  same  in  the 
smaller  and  in.  the  larger  sizes.  If  a  number  of  transformers  all 
having  the  same  relative  proportions  are  constructed,  their  weights 
and  consequently  their  volumes  and  losses  will  be  in  proportion  to 
the  cube  of  their  dimensions.  Their  outside  surface  and,  there- 
fore, their  relative  heat  radiating  abilities  will  increase  only  in  pro- 
portion to  the  square  of  their  dimensions.  Thus  comparing  two 
transformers  whose  dimensions  are  as  two  to  one,  the  larger  will 
weigh  eight  times  as  much  as  the  smaller,  and  will  in  consequence 
have  a  loss  eight  times  as  great.  It  will,  however,  have  only  four 
times  the  radiating  surface  and  the  temperature  rise  above  the 


FIG.  146. 


THE  TRANSFORMER 


199 


room  temperature  will,  therefore,  be  twice  as  great  as  in  the  smal- 
ler transformer.     The  problem  of  cooling  the  larger  sizes  of  trans- 
formers is,  therefore,  a  much  more  serious  one  than  in  the  case  of 
the  smaller  sizes.     The  same 
problem  is  met  with,  but  to  a 
lesser  extent,  in  the  design  of 
all    classes   of   electrical   ma- 
chinery.    In  dynamos  not  so 
much  difficulty  is  experienced, 
since  in  the  larger  machines 
there  is  not  the  same  incen- 
tive to  employ  the  same  rela- 
tive shape  as  in  the  smaller 
ones. 

One  expedient  to  overcome 
this  difficulty  is  the  provision 
of  a  corrugated  surface  for 
the  containing  case.  The 
corrugations  are  sometimes 
made  as  deep  as  4  in.  or  more. 
Soon,  however,  a  point  is 
reached  where  further  deepen- 
ing of  the  corrugations  is 
without  much  effect,  and 
some  other  method  must  be 
adopted  to  increase  the  cool- 
ing surface.  One  successful 
way  of  doing  this  is  illus- 
trated in  Fig.  146.  As  will 
be  seen  from  the  illustration, 
numerous  tubes  are  provided 
extending  from  the  bottom  to 
the  top  of  the  case.  The  oil 
in  the  tubes  becomes  cooler 
than  that  in  the  interior,  and 
descends,  thus  setting  up  a  FIG.  147. 

circulation.     The  greatly  in- 
creased radiating  surface  is  sufficient  to   dissipate   all  of  the 
heat  generated  without  undue  rise  of  temperature. 

Another  effective  method  makes  use  of  a  coiled  pipe  immersed 
in  the  oil  near  the  top  of  the  containing  case.     Cold  water  is 


200      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

forced  through  this  coil,  and  this  cools  the  oil  in  its  vicinity, 
causing  it  to  descend,  and  thus  set  up  a  circulation.  This 
method  is  naturally  largely  used  in  transformers  in  water-power 
plants,  as  a  plentiful  supply  of  water  under  pressure  is  always  at 
hand. 

In  the  last-mentioned  method  there  is  some  possibility  that 
the  water  will  freeze  and  burst  the  coil.  In  this  event,  the  wind- 
ings of  the  transformer  would  probably  be  injured.  In  some  in- 
stallations this  danger  is  avoided  by  pumping  the  oil  itself  from 
the  cases  of  the  transformers  and  leading  it  through  a  system  of 
air-cooled  tubes  or  through  a  radiator  in  which  it  is  cooled.  A 
water-cooled  transformer  is  shown  in  Fig.  147. 

Transformers  intended  for  comparatively  moderate  pressures, 
generally  not  in  excess  of  40,000  volts,  frequently  are  not  immersed 
in  oil  and  are  cooled  by  air  blown  through  them  by  means  of  a 
motor-driven  fan.  A  trench  is  provided  over  which  all  of  the 
transformers  are  so  placed  that  the  air  from  the  trench  can  es- 
cape only  by  passing  through  the  transformers.  Numerous 
ventilating  ducts  are  provided  in  the  latter,  and  every  effort  is 
made  to  provide  a  free  passage  for  the  air. 

189.  Losses  and  Efficiency  of  Transformers. — There  are  two 
losses  in  a  transformer,  the  fixed  loss  and  the  copper  loss.  The 
former  comprises  the  hysteresis  and  eddy-current  losses  and 
was  treated  in  Art.  180.  As  there  explained,  these  losses  are 
practically  constant,  no  matter  what  the  load. 

The  copper  loss,  on  the  other  hand,  is  proportional  to  the  square 
of  the  current  and  consequently  to  the  square  of  the  load. 

The  fixed  loss  is  readily  measured  by  connecting  a  wattmeter  in 
the  primary  circuit  of  the  transformer,  the  secondary  being  on 
open  circuit.  The  applied  voltage  must  be  the  rated  voltage. 
To  get  the  copper  loss  we  measure  the  resistance  of  primary  and 
secondary  by  voltmeter  and  ammeter  or  otherwise.  The  full-load 
current  is  readily  ascertained  from  the  name  plate  or  by  a  simple 
calculation. 

For  example,  assume  a  transformer  rated  100  k.v.a.,  2200-220 
volts,  60  cycles.  The  full-load  primary  current  is: 

100,000  ^  2200  =  45.5  amp. 

% 

The  secondary  current  may  be  taken  as  ten  times  as  great  or 
455  amp.  This,  while  not  strictly  exact,  is  near  enough  for  the 
purpose.  The  fixed  loss  is  found  to  be  1.3  kw.,  the  resistance  of 


THE  TRANSFORMER 


201 


the  primary  is  0.33  ohm;  that  of  the  secondary  0.0038  ohm.     The 
calculations  to  determine  full-load  efficiency  are  as  follows: 

Fixed  loss  =      1300  watts 

PR  primary      =  45.52  X  0.33       =       684  watts 
PR  secondary  =    4552  X  0.0038  =        787  watts 


Total  loss 


2771  watts  or 

2.77  kw. 
100.00  kw. 
102.77  k.w. 


Efficiency  = 


=     97.34  per  cent. 


Output  (at  100  %  power  factor) 
Input          =  output  -f-  losses 
output 
input 

In  a  similar  manner  the  efficiency  for  any  other  load  may  be 
computed. 

190.  Connection  of  Transformers. — Single  Phase. — As  a 
matter  of  convenience,  transformers  are  usually  provided  with 


FIG.  148. 

two  secondary  windings.  These  have  the  same  number  of  turns 
and  consequently  generate  the  same  voltage,  frequently  110  volts. 
The  two  secondaries  may  be  connected  in  any  one  of  the  three 
ways  shown  in  Fig.  148.  As  shown  at  A,  the  two  secondaries  are 
connected  in  series  and  the  terminal  voltage  is  double  that  of  one 
coil.  If  a  voltage  of  110  is  desired  the  connection  B  is 
used.  The  current-carrying  capacity  of  the  transformer  is 
double  that  of  the  transformer  connected  as  at  A  since  the  two 
coils  are  in  parallel.  Since  the  voltage  is  halved,  the  capacity 
is  the  same.  The  connection  C  is  the  same  as  the  A  except  that 
the  neutral  wire  is  connected,  giving  a  three-wire  system. 


202      PltlXCH'LKX  Oh'  DYNAMO  ELECTRIC  MACHINERY 


191.  Two-phase  Connections. — The  ordinary  method  of  con- 
necting transformers  to  a  two-phase  circuit  is  shown  under  A  in 
Fig.  149.  Each  transformer  is  connected  to  one  of  the  phases  in 
the  same  way  that  a  transformer  would  be  connected  to  a  single- 
phase  line.  There  is  usually  no  connection  between  the  trans- 
formers. The  three-wire  connection  shown  under  B  of  the  same 
figure  is  occasionally  used.  The  voltage  across  the  two  outside 
wires  in  this  case  is  equal  to  the  voltage  of  either  transformer 
multiplied  by  \/2. 


J                   J 

Phase  A 

A 

j 

B 

J                          J             ] 

Phase   B 

00000 

^00000. 

00000  j 

.00000. 

0000() 


TRffiW\rfOlFOlftF 

f-110V-4<-110V-v 
156V 


FIG.  149. 

192.  Three-phase  Connections. — To  change  the  voltage  of  a 
three-phase  circuit,  three  transformers  are  usually  employed, 
although  two  may  be  used  as  is  pointed  out  later.  Perhaps  the 
commonest  arrangement  is  that  shown  under  A  in  Fig.  150. 
The  three  transformers  are  connected  in  delta  on  both  the  pri- 
mary and  the  secondary  sides.  It  may  be  assumed  that  the  ratio 
of  transformation  is  ten  to  one  and  that  the  primary  voltage  is  2200. 
It  is  evident  that  the  secondary  voltage  of  each  transformer  will 
be  220  volts  and  since  they  are  connected  in  delta,  the  line  voltage 
will  also  be  220. 

In  B  'of  Fig.  150  are  shown  three  transformers  connected  in 
star  on  both  the  primary  and  secondary.  The  voltage  across 
each  primary  winding  will  not  be  the  line  voltage,  but  this  voltage 
divided  by  \/3-  Thus  with  the  same  assumptions  as  before,  the 
voltage  across  the  terminals  of  each  transformer  will  be  2200  -f-  \/3 
=  1270  volts.  Since  the  ratio  of  the  transformers  is  ten  to  one, 
the  voltage  across  each  secondary  winding  will  be  127  volts. 


THE  TRANSFORMER 


203 


Since  the  secondaries  are  also  connected  in  star,  the  line  voltage 
will  be  127  X  \/3  =  220  volts. 

With  this  connection  unless  the  three  transformers  are  iden- 
tical, the  voltage  drops  across  the  windings  will  not  be  the  same 


J                           J 

2t°°  4o 

1 

A 

B 

«-4270^/ 

(sms&J 

\MfiW 

UamJ 

SW&J 

--QP.QP-Q.^ 

-220-  -220* 
<— 220— > 


t-  127-, 


220 


» 


-220-> 


220 


FIG.   150. 


and  one  or  more  of  the  transformers  will  be  operating  at  a  higher 
voltage  than  that  for  which  it  was  designed.  This  connection 
is,  therefore,  little  used. 


]       J 

2200     | 

A 

JJMOJU 

B 

L0j*mJ 

..QQQ_QflJ         UL0_M&y 

U&fl&U 

UMAttJ 

427*+127* 


-f— 127- 


"oToTnn 


381- 


-381- 


Fio.  151. 


In  A  of  Fig.  151,  the  transformers  are  connected  in  star  on  the 
primary  side  and  in  delta  on  the  secondary.  Each  primary 
winding  has  impressed  upon  it  a  voltage  of  1270.  Since  the 


204      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


secondaries  are  connected  in  delta,  the  line  voltage  is  the  same 
as  the  transformer  voltage,  or  127. 

In  B  of  the  same  figure  the  primary  is  in  delta  and  the  sec- 
ondary in  star.  The  secondary  voltage  of  each  transformer  is  220 
volts  and  since  they  are  connected  in  star  the  line  voltage  is 
220  X  \/3  =  381  volts. 


PIG.  152. 

Connections  of  the  type  indicated  in  Fig.  151  are  frequently 
used  in  long  distance  transmission  lines.  When  a  line  is  first 
installed  the  load  may  be  light  and  the  transformers  at  both  ends 
of  the  line  may  be  connected  in  delta  on  both  sides.  Later, 
when  the  load  has  increased  to  such  an  extent  as  to  warrant  it, 
the  high  voltage  sides  may  be  reconnected  in  star.  This  will 
increase  the  line  voltage  73  per  cent.,  leaving  the  sending  and 


THE  TRANSFORMER 


205 


receiving  voltage  the  same.  On  the  other  hand,  these  connec- 
tions are  rarely  used  for  general  distribution  systems  as  they 
give  rise  to  odd  voltages  unless  special  windings  are  used. 

193.  Three-phase  Transformers. — Instead  of  using  three  sepa- 
rate transformers  connected  as  shown  in  the  previous  diagrams 
to  transform  a  three-phase  current,  it  is  entirely  possible  to  com- 
bine the  transformers  in  one  structure.  Such  a  transformer  is 
shown  in  Fig.  152.  Each  phase  is  wound  upon  one  of  the  three 
legs.  The  three  fluxes  in  the  legs  will  differ  in  phase  by  120°. 
The  flux  in  the  yokes  connecting  the  legs  together  will  be  the 
resultant  of  the  three  fluxes. 

By  building  a  transformer  in  this  manner,  a  large  saving  in 
labor  and  material  is  effected.  The  transformer  is  somewhat 


<•             °°on            > 

L&H&&&&MaO££/~ 

KQQQOOQOQQQQQOO. 

A 
220 

-220 


00000000000000 
B 

-220 


FIG.   153. 

cheaper  and  slightly  more  efficient.  The  floor  space  required  is 
considerably  reduced.  Perhaps  the  greatest  disadvantage  of  the 
three-phase  transformer  is  the  fact  that  in  case  of  trouble  the 
whole  unit  must  be  taken  out  of  service.  With  three  separate 
transformers  it  is  usually  necessary  to  remove  only  one  of  the 
three.  The  amount  of  capital  tied  up  in  spare  units  is  thus 
somewhat  less.  Moreover,  if  the  three  units  are  connected  in 
delta  on  both  sides,  it  is  possible  to  operate  with  only  two  of  the 
three  at  a  decreased  load.  This  is  explained  in  the  following 
sec ton. 

194.  The  Open-delta  Connection.— Two  transformers  con- 
nected as  shown  in  Fig.  153,  may  be  used  to  transform  the  voltage 
of  a  three-phase  line.  It  is  evident  that  the  voltage  across  the 


206      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


secondary  of  transformer  A  will  be  220  (assuming  that  the  ratio 
of  the  transformer  winding  is  ten  to  one),  and  the  same  will  be 
true  of  B.  The  voltages  of  A  and  B  will  differ  in  phase  by  120°. 
Therefore  the  voltage  across  the  two  outside  wires  in  the  figure 
will  be  the  vector  sum  of  two  voltages  of  220  volts  each  differing 
in  phase  120°.  This  sum  will  also  be  220,  and  there  is  a  three- 
phase  voltage  at  the  terminals  of  the  secondary. 

This  connection  is  sometimes  convenient  when  a  small  amount 
of  power  is  to  be  transformed.  It  would  hardly  be  used  in  large 
work  since  even  with  100  per  cent,  power  factor  on  the  secondary 
the  voltages  and  currents  in  the  transformers  will  not  be  in  phase. 
The  power  capacity  of  the  transformers  is  therefore  reduced. 


FIG.  154. 

The  voltage  regulation  is  also  poor  since  the  current  may  be  lag- 
ging in  one  transformer  and  at  the  same  time  leading  in  the  other. 

195.  Transformation  of  the  Number  of  Phases. — At  the  pres- 
ent time  no  method  exists  for  transforming  from  single  phase  to 
polyphase  or  vice  versa  without  the  use  of  rotating  apparatus. 
Of  course,  a  transformer  can  be  connected  to  a  polyphase  line 
and  take  single-phase  current  from  it,  but  the  current  in  the  line 
will  also  be  single  phase. 

It  is,  however,  a  simple  matter  to  change  from  any  number  of 
phases  greater  than  one  to  any  other  number  greater  than  one. 
In  Fig.  154  is  illustrated  the  method  of  changing  from  two  to 
three  phases  or  vice  versa.  Two  transformers  are  used.  The 
primaries  are  identical  but  the  secondary  of  one  has  only  86.6  per 
cent,  as  many  turns  as  that  of  the  other.  The  transformer  with 


THE  TRANSFORMER  207 

the  greater  number  of  secondary  turns  has  a  connection  brought 
out  from  the  middle  of  its  secondary  winding.  The  connections 
are  as  shown  at  the  left  of  Fig.  154. 

The  action  will  be  readily  understood  from  the  vector  diagram 
at  the  right  of  the  figure.  Assuming  that  the  two-phase  line  is 
the  primary,  the  secondary  voltages  will  differ  90°  in  phase,  and 
since  one  winding  is  connected  to  the  center  of  the  other,  the  dia- 
gram will  be  as  shown.  Assuming  that  the  voltage  from  A  to  B 
is  100,  that  from  C  to  D  will  be  86.6,  since  the  turns  are  assumed 
to  be  in  the  ratio  of  100  to  86.6.  The  voltage  from  A  to  D  or 
from  D  to  B  will  be  50.  The  voltage  from  A  to  C  or  from  C  to 
B  will  be  the  resultant  of  the  two  voltages  and  will  be  equal  to 

V(86J52  +  502)  =  100 

Since  the  three  voltages  A  B,  BC,  and  CA  are  the  same,  a  three- 
phase  system  results.  The  connection  will  work  equally  well  to 
transform  from  three  to  two  phase.  This  is  known  as  the 
Scott  connection. 

PROBLEMS 

87.  A  certain  transformer  is  rated  10  kv-a.,  primary  voltage  2200,  second- 
ary voltage  220.     When  connected  to  2200-volt  mains  of  the  proper  fre- 
quency the  input  is  80  watts,  the  output  being  zero.     The  resistance  of  the 
primary  is  2.95  ohms,  that  of  the  secondary  0.0306  ohm.     Calculate  the 
efficiency  at  %,  ^£,  %>  full  load  and  1*4  load.     Also  calculate  the  maximum 
efficiency.     This  will  occur  when  the  copper  loss  and  the  iron  loss  are  equal. 

88.  The  above  transformer  is  used  on  a  distributing  system  and  is  con- 
nected to  the  primary  mains  at  all  times.     It  is  used  an  average  of  3  hr. 
per  day  at  full  load.     Determine  the  value  of  the  power  lost  in  iron  loss 
and  in  copper  loss  in  1  year  if  it  costs  1  cent  per  kilowatt-hour  to  generate 
the  power. 

89.  Three  transformers  are  used  to  step  up  the  voltage  of  a  three-phase 
line.     The  ratio  of  the  turns  on  the  primary  to  those  on  the  secondary  is  1 
to  10.     The  transformers  are  connected  in  delta  on  the  primary  and  in 
"  Y"  on  the  secondary.     If  the  primary  voltage  is  6600,  what  is  the  second- 
ary voltage? 

90.  Using  the  same  transformers,  what  would  be  the  secondary  voltage 
if  the  transformers  were  connected  in  star  on  the  primary  and  in  delta  on 
the  secondary? 


CHAPTER  XVI 
SYNCHRONOUS  GENERATORS  AND  MOTORS 

196.  General  Construction. — A  perspective  view  of  a  syn- 
chronous machine  is  shown  in  Fig.  155  and  separate  views  of  the 
armature  and  field  are  shown  in  Figs.  156  and  157.  This  is  a 
modern  type  in  which  the  field  is  always  the  revolving  element. 
Figure  158  illustrates  an  older  type  in  which  the  armature  re- 


FIG.  155. 

volves  and  the  field  is  at  rest.  This  form  is  rarely  built  at  the 
present  time.  The  principal  reasons  for  this  have  already  been 
given. 

Any  synchronous  machine  may  be  used  either  as  a  generator 
or  as  a  motor.  In  fact,  this  is  true  of  all  dynamo-electric  ma- 
chines, whether  operated  by  alternating  or  direct  currents.  All 
that  is  required  to  change  generator  action  into  motor  action  is 

208 


SYNCHRONOUS  GENERATORS  AND  MOTORS  209 


FIG.   156. 


RINGS  SICTIONALIZED 

TO  FACILITATE  REMOVAL 

OF  POLE  PIECE 


DESIGNED  FOR 
DOUBLE  SPEED 


COIL  CEMENTED  INTO 
A  HARD  COMPACT  MASS 


FIBER 
VTION 
BETWEEN  COILS 


FIG.  157. 


ii 


210      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


that  the  current  in  the  armature  should  be  reversed,  the  direction 
of  the  flux  from  the  field  poles  remaining  the  same. 

In  Fig.   159  is  shown  a  section  of  a  synchronous  machine. 
N  and  S  represent  the  field  poles.     These  may  be  of  either  solid 


FIG.  158. 


or  laminated  construction.  The  practical  difference  is  not  great, 
each  construction  having  advantages  from  certain  standpoints. 
The  armature  is  represented  as  a  broken  rectangle  above  the 


FIG.  159. 


field  poles.  It  is  always  constructed  of  laminated  iron,  as  other- 
wise the  heat  due  to  eddy-current  losses  would  be  so  great  as  to 
destroy  the  machine.  The  conductors  are  placed  in  slots  parallel 


SYNCHRONOUS  GENERATORS  AND  MOTORS     211 

to  or  nearly  parallel  to  the  pole  faces,  or  as  shown  in  the  diagram, 
perpendicular  to  the  plane  of  the  paper. 

197.  Action  as  a  Generator. — In  considering  the  elementary 
action  of  the  machine  as  a  generator,  assume  that  the  number  of 
these  conductors  is  very  great,  and  that  each  is  connected  to  its 
own  receiving  circuit,  and  let  these  circuits  be  exactly  alike.  For 
the  present,  assume  that  they  are  all  non-inductive. 

It  will  be  evident  that  the  e.m.f.  induced  will  be  greatest  in 
those  conductors  which  are  di- 
rectly  under   the   center  of   a  — ^-    ~\^          ^/       — ^ — 
pole  face,    and    zero    in   those  FlG   16Q 

midway  between  the  poles.    At 

intermediate  points,  the  e.m.f.  will  be  in  the  same  direction  as 
that  of  the  conductors  under  the  center  of  the  pole,  but  will  be 
of  lesser  value. 

If  opposite  each  point  of  the  pole  face,  we  plot  a  point  whose 
distance  from  the  line  AB  is  proportional  to  the  e.m.f.  induced 
in  the  conductor  and  join  all  of  these  points  by  means  of  a  smooth 
line,  a  curve  of  the  general  shape  of  that  marked  e.m.f.,  in  Fig. 
159,  is  obtained.  As  the  field  moves  with  respect  to  the  armature, 


FIG.  161. 

this  curve  will  retain  the  same  position  with  respect  to  the  field 
poles.  Thus  if  the  armature  stands  still  and  the  field  revolves, 
the  curve  will  also  revolve  at  the  same  rate.  If,  on  the  contrary, 
the  armature  is  the  revolving  part,  the  curve  will  be  stationary  in 
space.  This  curve  may  be  called  the  curve  of  space  distribution 
of  e.m.f.  It  should  be  carefully  distinguished  from  the  curve  of 
time  variation  of  e.m.f]  although  here,  they  are  of  the  same  shape, 
but  this  would  not  in  general  be  true. 


212      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

198.  Space  Curve  of  E.M.F. — The  curve  of  e.m.f.  distribution 
may  assume  various  shapes.  Figure  160  shows  its  approximate 
shape  when  the  synchronous  machine  is  so  constructed  that  the 
air  gap  is  of  the  same  length  at  all  parts  of  the  pole  face.  This 
results  in  a  nearly  uniform  value  of  the  flux  at  all  parts  of  the 
pole  face  and  consequently  in  a  nearly  uniform  value  of  the  e.m.f. 
as  long  as  the  conductor  is  moving  through  this  uniform  flux. 
In  the  spaces  between  the  poles  there  will  be  little  flux,  and  the 
e.m.f.  induced  will  be  correspondingly  feeble.  Figure  161 
illustrates  the  type  of  wave  induced  in  case  the  pole  is  very  narrow 
and  the  spaces  between  the  poles  correspondingly  large. 

Figure  162  shows  a  sine  wave  of  e.m.f.  distribution.  To 
obtain  this  shape,  the  flux  must  also  have  a  sinusoidal  distribu- 
tion. To  accomplish  this,  the  pole  faces  are  rounded  somewhat 


FIG.  162. 

as  shown  in  Fig.  159.  This  causes  the  flux  to  be  strongest  at  the 
center  of  the  pole  faces  and  to  become  gradually  weaker  as  the 
point  midway  between  the  poles  is  reached.  It  should,  however, 
not  be  assumed  that  it  is  necessary  to  have  this  distribution  of  the 
flux  in  order  to  have  a  sine  wave  of  terminal  e.m.f.  in  the  machine. 
It  is  entirely  possible,  by  combining  several  non-harmonic  waves 
of  e.m.f.,  to  produce  a  resultant  sine  wave.  In  general,  it  is 
desirable  that  the  machine  should  have  a  wave  of  e.m.f.  distri- 
bution like  that  of  Fig.  159,  but  it  is  even  more  necessary  that 
the  terminal  wave  of  e.m.f.  should  be  sinusoidal.  However,  if 
the  curve  of  e.m.f.  distribution  is  sinusoidal,  the  curve  of  terminal 
e.m.f.  will  always  be  sinusoidal,  irrespective  of  the  connections 
employed,  since  two  or  more  sine  waves  always  add  together  to 
form  another  sine  wave. 

199.  Space  Curve  of  Flux  and  Current. — Since  the  motion  of 
the  conductors  through  the  flux  is  constant,  the  e.m.f.  at  any 
point  is  proportional  to  the  flux  at  that  point.  The  same  curve 


SYNCHRONOUS  GENERATORS  AND  MOTORS  213 

(taken  with  the  proper  ordinates)  which  shows  the  space  distri- 
bution of  e.m.f.  will  therefore  serve  as  the  space  curve  of  flux. 

Assuming  now  that  a  sine  wave  of  e.m.f.  distribution  has  been 
obtained,  and  that  each  conductor  is  connected  to  its  own  receiv- 
ing circuit,  a  curve  of  current  distribution  may  be  plotted  in 
addition  to  the  curve  of  e.m.f.  distribution.  If  all  the  receiving 
circuits  are  equal  and  in  addition  are  non-inductive,  the  curve  of 
current  distribution  will  be  sinusoidal  and  in '  phase  with  the 
curve  of  e.m.f.  distribution  as  indicated  by  the  dashed  line  of  Fig. 
159.  The  current  then  will  rise  and  fall  in  exact  .synchronism 
with  the  movement  of  the  field  poles  or  of  the  flux.  As  a  short 
and  convenient  means  of  designation  these  three  elements  of  the 
machine  may  be  called  the  flux  sheet,  the  e.m.f.  sheet,  and  the 
current  sheet.  These  three  sheets  may  be  regarded  as  being 
all  in  the  same  phase  and  as  having  the  same  shape.  If  the 
machine  is  of  the  revolving  field  variety,  all  three  sheets  revolve 
around  the  armature  at  synchronous  speed.  If  on  the  other  hand, 
the  field  magnet  is  stationary,  the  three  curves  remain  stationary 
in  space,  but  are  of  course  as  before  in  motion  with  respect  to  the 
armature. 

200.  Torque  in  a  Synchronous  Machine. — The  next  step  is 
to  examine  the  production  of  torque  in  a  machine  of  this  character. 
It  will  be  remembered  that  one  of  the  fundamental  facts  of  elec- 
tricity is  that  a  conductor  carrying  current  across  a  magnetic 
field  in  such  a  direction  as  to  be  perpendicular  to  the  direc- 
tion of  the  lines  of  induction,  is  subjected  to  a  force  expressed 
by  the  following  equation: 

F  =  ffi// 

where  F  is  the  force  in  dynes,  B  the  flux  per  square  centimeter, 
and  L  is  the  length  of  the  conductor  in  centimeters,  and  /  is  the 
current  in  absolute  units.  Expressed  in  the  customary  English 
units  of  pounds,  inches,  flux  per  square  inch,  and  amperes,  the 
equation  becomes, 

8.85 

w 

The  curve  of  space  distribution  of  pull  (or  torque)  is  obtained 
by  multiplying  the  product  of  the  current  and  the  flux  density 
at  any  given  point  by  a  constant.  This  curve  is  indicated  in  Fig. 
159.  Since  the  flux  and  the  current  change  directions  at  the 
same  points  the  pull  is  always  in  the  same  direction. 


214      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

Since  the  relative  positions  of  the  flux  sheet  and  the  current 
sheet  do  not  change,  it  is  evident  that  the  torque  will  be  constant 
and  consequently  the  power  input  and  output  of  the  machine  will 
also  be  constant.  In  other  words,  the  pull  changes  in  space  but 
not  in  time. 

In  the  foregoing  case,  when  the  machine  is  acting  as  a  generator, 
the  torque  is  in  such  a  direction  as  to  oppose  the  motion  of  the 
machine.  If  the  direction  of  all  of  the  currents  is  reversed, 
the  torque  will  also  be  reversed,  and  will  be  in  the  direction 
of  the  motion.  The  machine  will  then  be  a  synchronous  motor. 
Since  such  operation  generally  involves  the  presence  of  at  least 
two  synchronous  machines,  one  as  generator,  the  other  as  motor, 
the  case  is  somewhat  complicated.  The  additional  factors  which 
must  be  considered  will  be  treated  in  the  subsequent  pages. 

201.  Effect  of  Power  Factor  on  Torque. — Return  again  to  the 
conception  of  the  machine  as  a  synchronous  generator,  but 


Pull  or  Torque 


FIG.  163. 

instead  of  assuming  the  receiving  circuits  non-inductive,  let  them 
be  replaced  by  circuits  having  inductance  so  as  to  cause  the  cur- 
rent to  lag  behind  the  e.m.f .  Since  it  has  been  assumed  that  all 
the  receiving  circuits  are  alike,  each  current  will  lag  the  same 
amount,  and  the  net  result  will  be  that  the  curve  of  current 
distribution  will  be  moved  bodily  to  the  left  if  the  direction  of 
motion  of  the  field  is  from  left  to  right.  This  condition  is  shown 
in  Fig.  163. 

If  the  current  and  flux  are  of  the  same  maximum  values  as 
before,  the  torque  required  to  keep  the  generator  in  motion  will 
now  be  less.  In  Figs.  159,  163,  and  164,  the  curve  of  e.m.f.  may 
also  be  taken  as  the  curve  of  flux,  since  the  two  are  proportional. 
In  Fig.  159,  the  flux  and  the  current  are  in  all  cases  in  the  same 
relative  direction.  With  the  convention  adopted,  when  the 
curves  are  on  the  same  side  of  the  zero  line,  it  is  assumed  that  the 


SYNCHRONOUS  GENERATORS  AND  MOTORS  215 

torque  is  positive,  i.e.,  that  the  machine  is  acting  as  a  generator. 
In  Fig.  163,  however,  the  action  is  not  the  same  at  all  points  of 
the  periphery.  Thus  in  the  portion  ab,  the  flux  and  the  current 
are  in  opposite  directions  or  on  this  portion  of  the  periphery 
motor  action  exists  and  the  pull  on  the  field  is  in  the  direction 
from  left  to  right.  In  the  portion  be,  on  the  contrary,  the  pull 
is  from  right  to  left,  or  generator  action  exists.  The  interval  cd 
is  again  the  seat  of  motor  action,  de,  of  generator  action  and  so  on. 
The  net  torque  of  the  machine  will  be  the  torque  of  all  of  the 
sections  located  in  the  positions  corresponding  to  6c,  minus  the 
torque  of  all  such  sections  as  ab.  The  torque  required  to  keep 
the  machine  in  motion  is  therefore  reduced.  Yet  the  torque  of 
the  whole  machine  is  constant  during  the  whole  time.  The  fact 
is  that  at  certain  parts  of  the  periphery  there  is  a  pull  in  the 
direction  of  the  motion,  and  over  a  larger  part  of  the  periphery,  a 
pull  opposed  to  the  motion.  The  pull  is  then  on  the  whole  in 
opposition  to  the  motion,  or  the  machine  is  a. generator,  but  the 
pull  is  less  than  would  be  the  case  if  the  current  and  the  flux 
(and  consequently  the  e.m.f.)  were  in  the  same  phase. 

As  previously  explained,  if  the  current  and  the  e.m.f.  are  in 
the  same  phase,  which  is  equivalent  to  saying  that  the  flux 
distribution  curve  and  the  current  distribution  curve  are  in  the 
same  phase  as  shown  in  Fig.  159  the  power  is  represented  by  the 
equation 

P  =  El 

If  on  the  other  hand,  the  current  and  e.m.f.  are  not  in  phase,  the 
expression  becomes 

P  =  pEI 

in  which  p  is  a  number  not  greater  than  1  and  is  known  as  the 
power  factor.  It  is  often  difficult  to  understand  how  a  large 
current  and  a  large  e.m.f.  may  exist  in  a  circuit  at  the  same  time 
that  the  power  is  little  or  nothing.  The  foregoing  explains  how 
this  happens  in  a  generator  supplying  an  inductive  circuit. 

202.  The  Case  of  Zero  Power  Factor. — Fig.  164  shows  the  con- 
ditions when  the  lag  of  the  current  behind  the  e.m.f.  is  90°.  It 
will  be  seen  that  the  portion  ab  of  the  curves  is  now  exactly  equal 
to  the  portion  be.  The  positive  and  the  negative  parts  are  there- 
fore equal  and  the  net  torque  and  consequently  the  net  power  is 
zero.  A  further  lag  of  the  current  would  result  in  the  negative 
portion  of  the  torque  becoming  greater  than  the  positive  or  the 


216      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

machine  would  be  acting  as  a  motor.  It  would  not  be  possible  by 
using  inductance  to  obtain  a  circuit  in  which  the  lag  was  90°  or 
more,  since  there  would  always  be  some  loss  in  the  circuit  which 
would  cause  the  power  to  be  positive.  It  is,  however,  entirely 
possible  to  obtain  such  a  condition  when  two  machines  are  operat- 
ing in  parallel  on  the  same  load.  If  the  throttle  of  the  steam  engine 
connected  to  one  of  the  generators  be  gradually  closed,  the  power 
given  to  that  machine  will  be  gradually  reduced.  If  this  be 
carried  far  enough,  the  power  as  indicated  by  a  wattmeter  will 
decrease  and  finally  reach  zero.  Closing  the  throttle  further  will 
cause  the  power  to  reverse,  or  the  machine  will  operate  as  a  motor. 
At  the  time  when  the  power  indicated  by  the  wattmeter  is  zero, 


FIG.  164. 

current  will  in  general  still  be  flowing.  The  power  factor  is 
then  zero.  The  details  of  this  action  will  be  better  understood 
when  the  action  of  the  machine  as  a  synchronous  motor  has  been 
more  fully  explained. 

203.  Influence  of  the  Number  of  Phases. — Heretofore  it  has 
been  considered  that  the  number  of  conductors  per  pole  and  the 
number  of  phases  was  infinite  or  at  least  very  great,  and  that  each 
was  connected  to  its  own  receiving  circuit.  In  actual  synchron- 
ous machines,  the  number  of  conductors  per  phase  is  compara- 
tively small,  and  these  are  connected  to  form  a  small  number  of 
phases.  Usually  the  conductors  are  separated  into  either  one, 
two  or  three  groups  per  pole.  These  conductors  are  then  con- 
nected to  form  a  single-,  two-  or  three-phase  winding.  Of  these, 
the  three-phase  winding  is  the  one  generally  used.  The  two- 
phase  winding  was  common  a  few  years  ago,  but  is  rarely  seen 
now,  while  the  single-phase  winding  is  very  rarely  used  except 
for  machines  furnished  to  plants  where  it  is  desirable  that  addi- 
tional machines  should  conform  to  the  earlier  type  of  equipment. 


SYNCHRONOUS  GENERATORS  AND  MOTORS 


217 


Figure  165  shows  a  section  of  a  three-phase  machine.  There 
are  six  conductors  per  pole,  or  two  per  pole  per  phase.  In  prac- 
tice, except  in  the  case  of  very  small  machines,  there  are  usu- 
ally three  or  four  conductors  per  pole  per  phase,  although  two 
are  by  no  means  uncommon.  All  the  conductors  of  each  phase 
are  connected  in  series  by  connecting  one  of  the  a  conductors 
under  a  north  pole  to  one  of  the  a  conductors  under  the  adjoin- 


FIG.  165. 

ing  south  pole.     There  are  several  means  of  doing  this,  some  of 
which  were  explained  in  Chap.  XIV.  . 

It  will  be  seen  that  the  curve  of  e.m.f.  distribution  will  be  a 
sine  curve  as  before.  The  curve  of  current  distribution  or  the 
current  sheet  will,  however,  be  different.  This  is  apparent  on 
account  of  the  fact  that  all  of  the  conductors  in  one  phase  must 
have  the  same  current  flowing  in  them,  since  all  are  connected  in 
series.  The  result  is  that  the  current  sheet  assumes  the  stepped 
appearance  of  Fig.  165.  The  relation  of  the  three  currents  in 


234 

1  c  ' 


FIG.  166. 

time  phase  will  be  as  shown  in  Fig.  166.  The  current  sheet  of 
Fig.  165  is  shown  at  the  time  marked  "  1 "  in  Fig.  166.  An  in- 
stant later,  at  the  time  marked  "2,"  the  shape  of  the  current 
wave  will  be  different  since  now  the  current  in  phase  B  has  be- 
come zero  while  A  has  decreased  somewhat  and  at  the  same  time 
C  has  increased.  The  sum  of  the  three  currents  is,  however,  the 
same  as  before.  The  shape  of  the  current  wave  at  this  time  will 


218      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

be  as  shown  by  the  dotted  line  in  Fig.  165.  An  instant  later, 
at  the  time  marked  "3"  the  shape  will  be  the  same  as  at  the 
time  "  1 "  but  removed  still  farther  to  the  right.  At  intermediate 
times,  the  shape  of  the  current  sheet  will  be  between  that  cor- 
responding to  the  time  "1"  and  that  of  "2."  The  current  sheet 
as  a  whole  moves  steadily  to  the  right,  but  with  a  slight  change 
of  shape  as  it  progresses. 

This  discussion  is  also  directly  applicable  to  the  induction 
motor.  The  windings  of  the  stator  of  an  induction  machine  and 
of  a  synchronous  machine  are  identical,  except  as  modified  by 
the  fact  that  the  induction  machine  is  frequently  wound  for  a 
lower  voltage  than  the  synchronous  machine.,  A  rotating  mag- 
netic field  is  set  up  by  the  rotating  current  sheet  in  the  case  of 
both  machines.  The  action  of  this  will  be  considered  later. 
It  may  be  well  to -repeat  that  the  stator  current  may  have  either 
a  magnetizing  or  a  demagnetizing  effect  upon  the  main  field, 
depending  upon  whether  it  is  a  lagging  or  a  leading  current. 
When  it  is  in  phase  with  the  e.m.f.  its  magnetizing  effect  is  nearly 
zero. 

204.  Synchronous  Machines  in  Parallel. — In  practice,  it  is 
seldom  possible  to  operate  one  synchronous  machine  alone  on  a 
line.  This  is  often  due  to  the  fact  that  it  is  impossible,  or  at 
least  impracticable,  to  build  machines  of  a  capacity  great  enough 
to  take  care  of  the  entire  output  of  a  station  as  in  the  case  of  the 
large  power  houses  at  Niagara  Falls.  In  any  event,  it  is  considered 
advisable  to  have  the  capacity  of  the  station  divided  into  several 
units,  so  that  the  station  may  operate  more  efficiently  at  light 
loads,  and  so  that  it  may  be  easier  to  have  reserve  units  in  case 
of  breakdown.  It  might,  however,  be  possible  to  divide  the  load 
between  the  various  machines,  so  that  each  would  operate  in- 
dependently of  the  others,  but  this  is  highly  undesirable,  and 
unnecessary. 

In  order  that  machines  should  operate  in  parallel  to  supply 
power  to  the  same  circuit,  it  is  necessary  that  the  e.m.fs.  of  all 
of  them  should  rise  and  fall  practically  together,  that  is,  the 
frequency  of  all  must  be  the  same.  This  in  turn  means  that  the 
machines  must  operate  at  exactly  the  same  speed  if  they  have 
the  same  number  of  poles,  or  if  the  numbers  of  poles  are  different, 
at  speeds  exactly  in  inverse  proportion  to  their  respective  num- 
bers of  poles.  This  relation  must  be  continued  as  long  as  the 
machines  are  in  parallel,  hence  it  is  quite  common  to  have 


SYNCHRONOUS  GENERATORS  AND  MOTORS  219 

several  machines  operate  for  days  at  a  time,  no  one  of  them  either 
gaining  or  losing  even  a  fraction  of  a  revolution  on  the  others. 
The  action  is  as  though  the  machines  were  connected  together 
by  means  of  invisible  gear  wheels.  Indeed,  if  these  gear  wheels 
are  regarded  as  being  slightly  flexible,  an  accurate  mechanical 
analogy  to  the  action  of  two  or  more  synchronous  machines  oper- 
ating in  parallel  is  obtained. 

When  machines  are  operating  together  in  parallel  in  this  man- 
ner, they  are  held  in  synchronism  by  the  inherent  electrical  action 
of  the  machines.  If  one  alternator  tries  to  get  ahead,  due  to 
an  increased  admission  of  steam  to  the  driving  engine  or  to  other 
causes,  it  automatically  takes  more  load  and  is  restrained  from 
increasing  its  speed,  at  least  permanently.  It  is  true  it  does 
revolve  faster  for  an  instant  until  it  is  slightly  ahead  of  the  others, 


-Machine  E.M.F. 
FIG.  167. 

but  the  farther  ahead  it  gets,  the  more  the  load  is  increased. 
The  amount  of  advance  is  always  very  small,  being  only  a  frac- 
tion of  a  pole  span.  On  the  other  hand,  if  the  load  is  reduced, 
the  machine  falls  back  slightly  in  phase,  thus  reducing  its  load 
and  restoring  the  balance.  Even  though  the  driving  power  is  en- 
tirely removed,  the  machine  will  not  stop,  but  will  continue  to 
revolve  as  a  motor  at  the  same  speed  as  before. 

205.  Relations  of  E.M.F.  and  Current. — In  Fig.  167  the  curve 
marked" Line e.m.f." represents  the  curve  of  applied  voltage  from 
the  line.  This  may  be  the  e.m.f .  of  one  machine  or  it  may  be  the 
resultant  applied  e.m.f.  due  to  several  machines.  The  back  e.m.f. 
of  the  machine  under  consideration  is  marked  "machine  e.m.f.," 
and  is  represented  as  being  exactly  equal  and  opposite  to  the  line 
e.m.f.  The  two  e.m.f.  waves  may  or  may  not  be  sine  waves.  It 
results  in  a  somewhat  simpler  diagram,  however,  if  they  are  taken 
as  sine  waves,  but  the  same  method  of  analysis  is  applicable  to 
any  form  of  wave. 

With  the  waves  equal  and  opposite,  as  shown,  they  will  be  in 


220      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

perfect  balance  at  all  times  and  there  will  be  no  tendency  for 
current  to  flow  through  the  machine,  and  the  machine  will  develop 
no  power. 

Suppose  now  that  the  driving  force  be  removed  from  the  ma- 
chine considered,  say  by  closing  the  throttle  of  the  steam  engine 
driving  it.  The  first  tendency  of  the  machine  will,  of  course,  be 
to  stop.  It  will  actually  drop  back  a  little  in  step  until  its  e.m.f. 
is  no  longer  directly  opposed  to  that  of  the  line.  This  is  shown 
in  Fig.  168.  The  two  e.m.fs.  will  now  no  longer  balance  one 
another.  If  their  difference  at  each  point  is  plotted,  the  curve  of 
difference  will  be  as  shown  in  the  curve  marked  "  Resultant 
e.m.f."  This  is  nearly  90°  different  in  phase  from  either  of  the 
original  curves.  It  will  be  a  sine  wave  if  the  machine  e.m.f. 
and  that  of  the  line  are  sinusoidal. 

This  unbalanced  e.m.f.  will,  of  course,  set  up  a  current  between 
the  two  machines.  In  such  a  circuit  the  reactance  will,  in  gen- 


-Machine  E.M.F. 


FIG.  168. 

eral,  be  far  greater  than  the  resistance  and  the  current  will,  there- 
fore, lag  nearly  90°  behind  the  resultant  e.m.f.  In  Fig.  168  it  is 
shown  as  lagging  approximately  80°.  Since  the  resultant  e.m.f. 
is  already  nearly  90°  out  of  phase  with  the  line  e.m.f.  and  the 
machine  e.m.f.,  and  since  the  current  lags  nearly  90°  behind  the 
resultant  e.m.f.,  the  current  will  be  brought  nearly  into  phase,  and 
phase  opposition,  respectively  with  the  line  and  the  machine  e.m.f. 
It,  therefore,  represents  power  in  connection  with  both  of  these 
e.m.fs.  Since  the  current  flows  in  general  in  opposition  to  the 
machine  e.m.f.,  the  machine  is  acting  as  a  motor.  The  machine 
or  machines  supplying  the  line  are,  of  course,  acting  at  the  same 
time  as  generators.  What  happens  then  is  that  the  machine  will 
drop  back  in  phase  (not  in  speed)  until  sufficient  current  flows  to 
supply  enough  torque  to  maintain  the  motion.  It  will  then  con- 
tinue to  operate  as  a  motor. 

If,  on  the  other  hand,  the  power  supplied  to  the  machine  under 


SYNCHRONOUS  GENERATORS  AND  MOTORS  221 

consideration  had  been  increased  instead  of  reduced,  the  ma- 
chine would  have  advanced  somewhat  in  phase,  the  resultant 
e.m.f.  and  the  corresponding  current  would  have  been  reversed, 
and  the  machine  instead  of  acting  as  a  motor  would  have  become 
a  generator.  It  is  thus  possible  to  increase  or  diminish  the  power 
output  of  a  synchronous  machine,  or  even  cause  it  to  act  as  a 
motor  by  changing  in  the  corresponding  manner  the  power  input 
to  the  machine.  All  this  is  accomplished  without  any  change  in 
the  field  current,  the  generated  voltage  or  the  speed  of  the 
machine. 

206.  Effect  of  Change  of  Field  Current. — A  change  in  the 
field  current  of  a  synchronous  machine  results  in  only  a  slight 
change  in  the  power  output  of  the  machine.  This  is  a  rather 
surprising  result  to  one  accustomed  only  to  the  action  of  continu- 
ous-current machinery.  It  is  true  that  changing  the  field  current 


Machine  E.M.F. 


Line  E.M.F/ 

FIG.  169. 

of  a  synchronous  machine  does  result  in  a  change  of  the  current 
delivered  by  the  machine,  but  the  power  remains  practically  the 
same.  Assuming  that  the  machine  and  the  line  e.m.fs.  are  equal 
and  opposite,  as  shown  in  Fig.  167,  increase  the  field  current  and 
the  generated  voltage  of  the  machine  under  consideration.  The 
result  will  be  an  unbalanced  voltage  as  shown  in  Fig.  169  in 
phase  with  the  machine  e.m.f.  This  will  cause  a  current  to  flow, 
and  this  current,  as  before,  will  lag  nearly  90°  behind  the  resultant 
e.m.f.  The  current  is  then  nearly  90°  in  phase  from  both  the 
applied  and  the  machine  voltage  and  consequently  represents 
little  power.  It  will  be  seen  that  with  the  machine  voltage  higher 
than  the  line  voltage,  the  resulting  current  is  leading  the  line  e.m.f. 
It  is  often  desirable  to  introduce  leading  current  into  a  system  in 
order  to  offset  lagging  current  due  to  induction  motors  or  to  other 
causes.  If  the  machine  voltage  had  been  lowered  instead  of 


222      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

raised,  the  resultant  e.m.f.  and  current  would  have  been  reversed 
and  the  current  would  have  been  lagging  instead  of  leading. 

207.  Effect  of  Regulation  of  Prime  Mover. — In  the  above, 
it  has  just  been  demonstrated  that  changing  the  field  current  of  a 
synchronous  machine  produces  little  or  no  effect  upon  its  power 
output.  That  this  is  so  could  have  been  readily  shown  by  a 
study  of  the  action  of  the  prime  mover,  driving  the  synchronous 
machine.  The  operation  of  the  governor  of  any  prime  mover  is 
dependent  upon  the  speed  of  the  machine.  In  general,  in  order 
that  a  steam  engine,  gas  engine,  water  turbine,  or  other  source 
of  power  should  develop  more  output,  it  is  necessary  that  its 
speed  be  reduced.  This  causes  the  governor  balls  to  drop  slightly, 
and  these  in  turn  actuate  suitable  mechanism  to  allow  the  admis- 
sion of  more  steam,  gas  or  water  as  the  case  may  be.  But  in  the 
case  of  a  prime  mover  driving  a  synchronous  machine,  there  can 
be  no  change  in  speed  as  long  as  the  speed  of  the  other  machines 
supplying  the  line  remains  the  same.  Since  varying  the  field 
strength  will  not  change  the  speed,  the  output  of  the  prime  mover 
will  not  change,  and  in  consequence  the  mechanical  input  of  the 
synchronous  machine  can  not  change  at  all  and  the  output  only 
very  slightly. 

When  the  load  upon  a  station  containing  several  synchronous 
machines  in  parallel  is  increased,  the  case  is  somewhat  different. 
The  speed  of  all  of  the  machines  will  decrease  the  same  amount, 
and  if  the  governors  are  perfectly  adjusted,  the  admission  of 
power  to  all  of  the  machines  will  increase  in  the  proper  proportion, 
leaving  all  the  machines  loaded  to  the  same  percentage  of  their 
rated  capacity.  If  the  governors  are  so  set  that  some  of  the  units 
increase  their  output  more  than  others  for  the  same  reduction  in 
speed,  the  increase  of  load  will  not  be  divided  equally  among  the 
machines,  and  those  whose  prime  movers  regulate  more  closely 
will  take  more  than  their  proportion  of  the  load.  In  certain  cases 
it  is  desirable  that  this  should  be  the  case.  Thus  if  one  or  more 
reciprocating  units  are  operating  in  parallel  with  one  or  more 
steam  turbines,  it  is  generally  considered  desirable  that  the  former 
should  operate  at  as  near  their  rated  load  as  possible  and  that  the 
turbines  should  take  the  fluctuations.  This  is  desirable  since  the 
efficiency  of  a  turbine  does  not  decrease  so  much  for  under-  or 
overload  as  does  that  of  a  reciprocating  engine.  The  result 
mentioned  can  be  secured  by  setting  the  turbine  governors  to 
regulate  more  closely  than  those  of  the  reciprocating  engines. 


SYNCHRONOUS  GENERATORS  AND  MOTORS 


223 


The  only  way  of  changing  the  load  on  one  of  a  number  of 
synchronous  machines  is  to  change  the  power  input  to  its  prime 
mover.  This  is  generally  done  by  changing  the  stiffness  of  a  spring 
comprising  part  of  the  governor  mechanism.  It  is  customary  in 
the  case  of  steam  turbines  to  mount  a  small  motor  on  the  frame 
of  the  turbine,  and  connect  this  with  the  governor  spring  in  such 
a  manner  that  the  latter  may  be  compressed  or  extended  by 
means  of  the  motor.  The  output  of  the  generator  can  then  be 
readily  controlled  by  means  of  a  small  double-throw  switch  on 
the  switchboard,  this  small  switch  being  so  connected  as  to  stop, 
start  or  reverse  the  small  motor. 

208.  Treatment  by  Means  of  Vectors. — The  results  described 
could  have  been  deduced  by  means  of  vectors  instead  of  the 


Line  E.M.F. 


Machine  E.M.F. 

FlG.    170. 


LineE.M.F. 


^Current 


'Resultant  E.M.F. 


Machine  E.M.F. 


FIG.  171. 


Line  E.M.F. 
-Current 


Machine  E.M.F. 


FlG.    172. 


curves  used  in  the  preceding  figures.  Indeed  the  method  would 
have  been  much  simpler,  although  essentially  the  same  as  that 
employed.  The  vector  method,  however,  is  not  nearly  so  clear  to 
most  as  a  consideration  of  the  curves  of  current  and  e.m.f.  as 
just  presented.  It  must  also  be  kept  in  mind  that  this  method  of 
analysis  is  applicable  to  any  form  of  wave,  while  the  vector 
method  of  treatment  is  applicable  to  sine  waves  only.  With 
these  qualifications  in  mind,  however,  the  vector  method  presents 
a  powerful  method  of  analysis,  and  possesses  the  great  advantage 
that  the  diagrams  are  in  general  so  simple  that  it  is  easy  to  carry 
a  picture  of  them  in  the  mind. 

Figures  170,  171,  172,  are  the  vector  diagrams  corresponding  to 
Figs.  167,  168,  and  169.     In  Fig.  170,  the  line  and  the  machine 


224      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

e.m.fs.  are  equal  and  opposite,  giving  as  before  a  zero  resultant. 
In  Fig.  171,  the  two  e.m.fs.  are  equal  but  the  driving  force  has 
been  removed  from  the  machine,  allowing  it  to  drop  back  slightly. 
The  resultant  e.m.f .  will  have  the  direction  as  shown,  and  the  cur- 
rent will  as  before  lag  behind  this  resultant  by  an  angle  of  almost 
90°.  This  brings  the  current  almost  into  phase  with  the  line 
e.m.f.  and  into  phase  opposition  to  the  machine  e.m.f.  The 
machine  will  then  operate  as  a  motor.  Figure  172  shows  what 
happens  when  the  field  current  is  increased  so  that  the  machine 
e.m.f.  is  greater  than  that  of  the  line.  The  resultant  e.m.f.  is 
in  phase  with  that  of  the  machine,  and  the  current,  since  it  lags 


\    LineE.M.F. 


\ 

\ 

Line  E.M.F. 

\ 

\ 

\ 

\     Resultant 

I—  jJ       E.M.F. 

\1 

./Resultant  E.M.F. 

^ 

r~~~*~ 

> 

Current 

\ 
LF.j 

Machine  E.M.F. 

\ 

a.  173. 

FIG.  174. 

Current 


Machine  E.M.F. 


almost  90°,  is  nearly  in  quadrature  with  both  the  line  and  the 
machine  e.m.f.  The  power  developed  is  then  nearly  zero. 

In  Figs.  173  and  174,  are  shown  the  vector  diagrams  respectively 
of  a  synchronous  machine  acting  as  a  generator,  and  of  a  machine 
with  its  generated  e.m.f.  less  than  that  of  the  line,  and  taking 
a  small  amount  of  power  as  a  motor.  The  construction  of  these 
will  be  readily  understood.  In  fact,  the  only  change  is  the  sub- 
stitution of  the  word  "line,"  for  "machine"  and  vice  versa.  It 
should  be  noted  that  in  the  latter  case,  the  current  consumed  by 
the  synchronous  machine  is  lagging. 

209.  The  Synchronous  Condenser.— The  ability  of  the 
synchronous  machine  to  take  either  a  leading  or  a  lagging 
current  by  using  a  relatively  strong  or  a  weak  field  current, 
is  frequently  used  in  practice  to  improve  the  power  fac-' 
tor  of  a  circuit.  A  machine  employed  for  this  purpose  is  called 


SYNCHRONOUS  GENERATORS  AND  MOTORS  225 

a  synchronous  condenser.  Thus  a  transmission  line  may  be 
employed  to  transmit  power  from  a  waterfall  to  a  distant  point 
where  the  power  would  in  most  cases  be  used  largely  to  drive 
induction  motors.  The  induction  motor  always  takes  current 
lagging  behind  the  e.m.f.,  the  lag  being  particularly  great  when  the 
load  is  light.  A  synchronous  motor  may  be  readily  used  to  correct 
the  power  factor.  Thus  Fig.  175  shows  the  line  e.m.f.  and  the 
current  taken  by  an  induction  motor.  An  overexcited  synchro- 
nous motor  operating  without  load  may  be  made  to  take  a  current 
leading  by  nearly  90°  as  indicated  in  the  diagram.  The  com- 
bined current  will  be  as  shown  by  the  line  marked  "resultant  cur- 
rent." This  it  will  be  seen  is  materially  less  than  the  current 
required  by  the  induction  motor  alone.  Hence  the  use  of  such  a 
synchronous  condenser  will  in 
many  cases  reduce  the  line  cur- 
rent and  consequently  the  line 
loss,  and  at  the  same  time  im- 
prove the  regulation.  More- 
over, the  synchronous  machine  / 
need  not  be  used  for  its  con-  / 
denser  effect  alone,  but  may  be  / 
made  to  carry  load  in  addition  / 


^Line  E.M.F. 


Induction  Motor 
Current 


Resultant  Current 


,.  /.  ^Synchronous  Motor  Current 

to  correcting  the  power  1  actor. 
It  can   be   shown   that   such   a 

machine  will  be  most  economical  considering  both  functions,  if 
the  wattless  and  the  power  components  of  its  current  are  made 
equal,  i.e.,  if  its  power  factor  is  made  70.7  per  cent.  It  will 
then  carry  approximately  70  per  cent,  of  its  rated  load  as  a 
motor,  and  at  the  same  time,  consume  70  per  cent,  of  the  watt- 
less current  it  could  carry  as  a  synchronous  condenser  alone. 

210.  Operation  with  Distorted  Waves. — It  will  be  seen  from  a 
consideration  of  the  vector  diagrams  that  by  a  proper  regulation 
of  the  field  current,  the  current  and  the  e.m.f.  of  a  synchron- 
ous machine  can  always  be  brought  into  the  same  phase  and 
consequently  that  the  power  factor  can  always  be  made  100 
per  cent.  It  must,  however,  be  kept  clearly  in  mind  that  the 
vector  diagrams  apply  only  to  sine  waves  and  are  meaningless, 
except  in  an  approximate  sense,  in  the  case  of  other  waves.  The 
diagrams,  in  which  the  waves  are  drawn  out  as  in  Figs.  167,  168, 
and  169,  are  applicable  to  waves  of  any  shape.  Thus  in  Fig. 
176,  we  have  a  line  e.m.f.  of  a  sine  shape  but  the  back  e.m.f.  of 

15 


226      PRINCIPLED  OF  DYNAMO  ELECTRIC  MACHINERY 

the  machine  is  distorted.  No  adjustment  of  the  field  strength 
would  cause  these  two  e.m.fs.  to  balance  one  another.  The  re- 
sultant e.m.f.  in  the  case  shown  is  a  sine  wave  of  three  times 
the  fundamental  frequency.  It  would  set  up  a  current  lagging 
nearly  90°  behind  itself,  and  likewise  of  triple  frequency.  The 
power  factor  would  in  this  case  be  far  from  unity,  since  no  matter 
how  light  the  load,  there  would  be  a  large  current  circulating  be- 
tween the  machines.  This  effect  is  most  noticeable  at  light  load, 
since  at  larger  loads,  its  effect  is  somewhat  masked  by  the  large 
load  current  in  phase  with  the  e.m.f.  The  writer  has  even  seen 
cases  where  the  addition  of  a  considerable  load  resulted  in  a 
marked  decrease  in  the  minimum  current  which  could  be  ob- 
tained by  field  adjustment.  This  was  probably  due  to  a  change 
of  the  wave  shape  of  the  motor  under  load. 


LineE.M.F, 


FIG.  176. 

211.  Hunting. — In  the  case  of  a  number  of  alternators  operat- 
ing in  parallel,  it  will  sometimes  be  noticeable  that  while  the  load 
and  current  from  the  whole  station  are  constant,  the  current  and 
power  outputs  of  some  individual  machines  are  very  unsteady. 
The  current  and  power  will  rise  together  then  drop  back  to 
minimum  current  and  perhaps  zero  power,  the  current  will  then 
rise  again  while  the  power  will  perhaps  reverse  and  become  nega- 
tive. The  machine  is  then,  of  course,  operating  for  the  moment 
as  a  motor.  This  action  is  called  hunting.  If  the  hunting  is 
less  violent,  there  will  be  merely  a  rise  and  fall  in  the  current  and 
power,  the  latter  never  reversing.  This  pulsation  of  power  and 
current  will  frequently  occur  with  a  definite  frequency,  the  time 
of  1  cycle  being  generally  from  1  sec.  to  about  10  sec.  The  same 
variation  of  power  and  current  will  frequently  occur  when  a 
machine  is  operating  as  a  synchronous  motor. 


SYNCHRONOUS  GENERATORS  AND  MOTORS  227 

The  cause  of  this  phenomenon  is  usually  something  external 
to  the  motor  or  generator,  and  some  machines  are  more  sensitive 
to  such  external  causes  than  are  others.  In  general  the  external 
cause  is  a  pulsation  in  the  power  supply  as,  for  instance,  the  varia- 
tion of  torque  during  the  revolution  of  a  single-cylinder  steam 
engine  or,  to  a  still  greater  degree,  of  that  of  a  single-cylinder  gas 
engine.  In  this  latter  case,  power  is  applied  during  only  one 
stroke  in  four,  and  even  then  not  at  a  uniform  rate.  When  a 
power  impulse  does  occur,  the  synchronous  machine  to  which 
the  gas  engine  is  connected  is  forced  ahead  in  phase,  so  that 
the  vector  diagram  becomes  like  that  of  Fig.  173.  Immediately 
thereafter  the  driving  force  is  removed  as  the  engine  starts  on  its 
idle  strokes  and  the  synchronous  machine  may  begin  to  act  as 
a  motor,  with  a  vector  diagram  like  that  of  Fig.  171.  When  the 
machine  surges  forward  it  is  liable  to  go  too  far;  this  increases  the 
generator  action  to  such  an  extent  that  the  machine  is  retarded 
greatly,  it  then  swings  back,  again  going  too  far  and  so  on.  The 
action  may  become  cumulative,  and  increase  to  such  an  extent 
that 'the  machine  pulls  out  of  step  with  the  other  machines. 
Hunting  is  also  sometimes  set  up  on  account  of  a  tendency  of 
the  engine  governor  to  hunt.  The  cause  of  this  is  that  the  gov- 
ernor, when  it  acts,  tends  to  go  too  far  and  admit  too  much 
steam  or  gas  to  the  cylinder.  The  action  is  very  similar  to  the 
hunting  of  the  alternator,  but  should  not  be  confused  with  it. 

212.  Prevention  of  Hunting. — The  best  way  to  avoid  hunting, 
is  to  avoid,  if  possible,  the  causes  which  may  induce  it.  Thus,  if 
it  is  practicable  to  drive  by  means  of  steam  or  water  turbines, 
there  is  little  prospect  of  trouble  from  this  source.  If  driving  by 
means  of  reciprocating  steam  engines  or  gas  engines  is  unavoid- 
able, much  may  be  done  to  remove  or  minimize  the  trouble.  A 
change  in  the  weight  of  the  flywheel  may  have  a  very  good 
effect.  The  change  may  involve  the  use  of  either  a  heavier  or  a 
lighter  wheel.  The  reason  for  this  will  be  plain  if  it  is  considered 
that  if  we  pass  continuous  current  through  one  section  of  the 
armature  winding  of  an  alternator,  the  field  at  the  same  time  being 
excited  by  means  of  continuous  current,  there  will  be  an  attraction 
tending  to  cause  the  field  to  assume  some  definite  position  with 
respect  to  the  armature.  If  the  field  and  the  armature  are  in 
some  other  position  than  this  one  of  rest,  and  current  is  turned 
on  to  the  two,  the  field  will  oscillate  about  its  position  of  rest 
with  a  certain  definite  period.  Similarly,  if  the  field  be  in  motion. 


228      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

and  some  cause  tends  momentarily  to  make  the  machine  run 
either  faster  or  slower  than  before  for  an  instant,  the  field  will 
tend  to  oscillate  with  this  same  period  in  addition  to  its  motion 
of  rotation.  Ordinarily,  this  oscillation  will  die  out  very  quickly, 
but  if  the  period  of  the  impulses  is  the  same  as  the  natural  period 
of  vibration  of  the  machine,  it  may  readily  occur  that  the  natural 
vibration  will  be  maintained  and  increased  until  the  hunting 
becomes  violent.  The  action  is  similar  to  that  involved  in  the 
motion  of  the  pendulum  of  a  clock,  wThich  is  kept  in  comparatively 
violent  motion  by  the  feeble  impulses  imparted  to  it  in  exact 
synchronism  with  its  motion.  A  change  in  the  weight  of  the 
flywheel  will  cause  the  period  of  vibration  of  the  moving  masses 
to  differ  from  that  of  the  impulses  communicated  to  them,  and 


Fm.  177. 

consequently  the  resonance  will  be  destroyed,  and  the  hunting 
either  completely  stopped  or  at  least  greatly  diminished. 

213.  Damping  Grids. — There  is  also  another  method  of  attack- 
ing the  problem.  If,  in  the  case  of  the  pendulum  mentioned, 
the  motion  were  to  take  place  in  some  liquid  such  as  water, 
the  oscillation  for  the  same  applied  force  would  be  much  weaker. 
A  similar  effect  can  be  obtained  in  a  synchronous  machine  by 
causing  the  production  of  eddy  currents  in  the  moving  mass 
whenever  it  moves  from  the  position  of  equilibrium.  Thus, 
considering  again  the  machine  with  continuous  current  in  both 
the  field  and  the  armature,  and  displaced  from  the  position  of 
rest,  it  is  evident  that  as  the  field  oscillates,  it  will  cut  the 
lines  of  induction  set  up  by  the  armature.  If  the  poles  are  solid, 


&YtfCHRONOUS  GENERATORS  AX1)  MOTOR*  229 

eddy  currents  will  be  produced.  This  requires  the  expenditure 
of  energy,  and  results  in  strongly  damping  the  motion.  The 
oscillation  will  then  quickly  die  out.  The  same  effect  can  be 
produced  by  providing  each  pole  with  a  copper  grid  as  shown  in 
Fig.  177.  This  is  sometimes  called  an  amortisseur  winding.  It 
is  similar  to  the  squirrel-cage  winding  of  an  induction  motor, 
and  like  the  latter  has  eddy  currents  induced  in  it  whenever 
it  cuts  across  the  flux. 

214.  The    Synchronous    Motor. — The    preceding    discussion 
applies  to  the  synchronous  machine  whether  used  as  a  generator 
or  as  a  motor.     When  a  machine  is  used  exclusively  as  a  motor, 
however,  certain  problems  arise  which  are  not  present  when  it  is 
operated  as  a  generator.     The  principal  difficulty  is  in  regard  to 
starting. 

215.  Methods  of  Starting. — Synchronizing  by  Means  of  Lamps. 
—If  a  single-phase  synchronous  machine  is  at  rest,  and  current 
is  applied  to  the  armature,  there  will  be  no  tendency  at  all  to 
rotate.     This  holds  whether  the  field  is  excited  or  not.     To  enable 
such  a  machine  to  operate,  it  is  necessary  that  it  be  started 
by  some  external  power,  brought  up  in  speed  until  its  frequency 
is  the  same  as  that  of  the  line,  and  then  be  connected  to  the 
line   when  it  is  in  such  a  phase  that  its  e.m.f.  is  directly  equal 
and    opposite   to   that   of   the   line.     The   driving   power   may 
then  be  removed  and  the  machine  will  continue  to  operate  as  a 
motor. 

To  be  sure  that  the  motor  is  at  the  proper  frequency  and 
phase  with  respect  to  the  line,  the  simplest  apparatus  that  can  be 
used  is  an  incandescent  lamp,  connected  as  shown  in  Fig.  178. 
If  connected  to  the  line  only  or  the  machine  only,  the  lamp  would 
light  up  and  remain  steadily  in  this  condition.  When  connected 
to  both  machine  and  line,  the  e.m.f.  applied  to  the  lamp  will  be 
the  vector  sum  of  the  e.m.fs.  of  the  two.  This  is  shown  in  Fig.  179 
where  one  vector  is  the  e.m.f.  of  the  line  and  the  other  that  of  the 
machine  about  to  be  synchronized.  For  convenience,  the  e.m.f. 
of  the  line  has  been  drawn  as  directed  inwardly  toward  the  center 
of  the  circle.  With  this  construction,  the  resultant  e.m.f.  is 
given  in  magnitude  by  the  line  so  marked.  If  the  frequency  of 
the  machine  to  be  synchronized  and  the  line  are  not  the  same,  the 
angle  between  the  two  vectors  is  constantly  changing,  or  it  may 
be  considered  that  one  of  the  vectors  (say  that  representing  the 
line  e.m.f.)  is  stationary  and  that  the  other  is  revolving  slowly 


230      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


around  the  center  point  in  a  counter-clockwise  direction  if  the 
machine  to  be  synchronized  is  operating  at  too  high  a  speed,  and 
clockwise  for  too  low  a  speed.  In  either  event,  it  is  evident 
that  the  resultant  e.m.f .  will  vary  in  value  from  zero  to  double  the 
value  of  either  of  the  two  main  e.m.fs.  The  lamp  will  then  alter- 
nately light  up  and  go  out,  making  a  complete  cycle  every  time 
the  machine  gains  or  loses  a  cycle  with  respect  to  the  line.  The 
lamp  will  then  show  two  things :  its  rate  of  lighting  up  and  going 
out  will  show  the  nearness  of  the  machine  to  synchronism,  and 
the  moment  of  darkness  will  indicate  the  phase  which  gives  zero 
resultant  e.m.f.,  and  consequently  the  proper  moment  for  closing 
the  switch. 


Resultant  E.M.F. 


FIG.  178. 


FIG.  179. 


In  practice,  it  would  not  be  desirable  to  use  a  switch  on  one  side 
only  of  the  circuit  as  indicated  in  Fig.  178.  To  make  possible  the 
use  of  a  two-pole  switch,  two  lamps  are  necessary,  one  connected 
across  each  side  of  the  switch.  With  a  three-phase  machine,  a 
three-pole  switch,  and  with  a  two-phase,  a  four-pole  switch 
would  be  needed.  It  would,  however,  be  unnecessary  to  provide 
more  than  two  lamps  in  either  case,  since  when  one  phase  is 
synchronized,  the  others  must  also  be  in  the  proper  relative 
position,  unless  the  connections  have  been  changed,  or  the 
direction  of  rotation  reversed  since  the  machine  was  connected. 

216.  The  Synchroscope. — With  either  of  the  foregoing  ar- 
rangements, there  is  some  difficulty  in  determining  the  moment 
of  exact  synchronism,  since  an  incandescent  lamp  will  not  light 
up  at  all  unless  about  15  per  cent,  of  its  rated  voltage  is  impressed 
on  its  terminals.  A  voltmeter  may  be  used  instead  of  the  lamps 
to  indicate  more  exactly  the  zero  of  the  e.m.f.  or  the  connection 
may  be  made  as  shown  in  Fig.  180.  This  diagram  shows  that 


SYNCHRONOUS  GENERATORS  AND  MOTORS  231 

at  the  moment  of  phase  opposition,  the  lamps  will  be  fully  lighted 
instead  of  being  dark.  This  condition  is  more  easily  recognized 
than  the  preceding.  After  the  machines  are  connected  together, 
the  lamps  will  in  this  case  remain  lighted. 

For  the  synchronizing  of  large  machines,  where  a  slight  mistake 
in  synchronism  might  be  disastrous,  an  instrument  called  a 
synchroscope  is  used.  This  indicates  by  means  of  a  pointer  re- 
volving around  a  dial  whether  the  incoming  machine  is  "fast" 
or  "slow"  and  also,  the  moment  of  exact  phase  opposition. 
These  can  be  built  of  large  size,  so  that  their  indications,  can  be 
read  in  any  part  of  a  large  engine  room.  Automatic  synchron- 
izers have  also  been  constructed  which  operate  to  close  the  main 
switch  when,  and  only  when, 
the  two  voltages  are  approxi- 
mately equal,  are  opposite  in 
phase,  and  the  frequencies 
are  nearly  the  same.  It  will 
be  obvious  that  the  preced- 
ing remarks  apply  equally 
well  to  the  synchronizing  of 
synchronous  generators  as  well  as  to  synchronous  motors. 

The  method  of  starting  described  is  practically  always  used  in 
the  case  of  synchronous  generators,  both  single  phase  and  poly- 
phase, as  a  prime  mover  is  always  present  to  bring  the  machine 
up  to  speed.  In  some  of  the  applications  of  synchronous  motors 
it  may  also  be  used.  Synchronous  motors  driving  direct-current 
generators  are  frequently  used  to  transform  alternating  current 
into  continuous  current.  In  this  case,  there  is  usually  present 
a  storage  battery  on  the  direct-current  line,  or  if  not,  there  may 
be  other  means  of  supplying  direct  current  to  the  line.  If  this 
is  the  case,  the  obvious  method  of  starting  is  to  use  the  continuous- 
current  machine  as  a  shunt  motor,  to  bring  the  synchronous 
machine  up  to  speed,  and  such  machines  are  normally  started  in 
this  manner. 

If  the  foregoing  plan  can  not  be  used,  it  is  sometimes  practicable 
to  install  the  synchronous  motor  with  a  friction  clutch  so  that  it 
may  be  started  without  load.  A  small  induction  motor  may  be 
mounted  on  the  shaft,  and  be  used  to  start  the  larger  machine. 
The  induction  motor  should  have  two  poles  less  than  the  syn- 
chronous machine,  so  that  it  will  be  able  to  bring  it  somewhat 


232      PRINCIPLED  or  DYXAMO  ELECTRIC  MACHINERY 

above  synchronous  speed.  This  method  works  well,  but  is 
somewhat  costly. 

217.  Direct  Starting  of  the  Synchronous  Motor. — A  single- 
phase  synchronous  motor,  has  absolutely  no  starting  torque.  If, 
however,  a  polyphase  machine  be  connected  to  the  line,  it  will 
develop  a  certain  torque  depending  in  value  upon  the  con- 
struction of  the  motor.  This  is  in  general  sufficient  for  start- 
ing the  motor  without  load. 

In  starting  in  this  way,  the  torque  is  greatest  if  the  field 
circuit  is  left  open.  The  torque  developed  is  due  principally  to 
induction  motor  action.  When  the  polyphase  current  is  applied 
to  the  armature,  a  revolving  magnetic  field  is  set  up  just  as  in 
the  case  of  the  induction  motor,  and  this  field,  cutting  across 
the  solid  pole  faces,  sets  up  currents  which  produce  torque  in 
the  same  manner  as  in  a  squirrel-cage  induction  motor. 

If,  as  shown  in  Fig.  177,  the  poles  are  provided  with  grids  to 
prevent  hunting  or  with  a  squirrel-cage  winding  for  the  same 
purpose,  the  starting  action  will  be  stronger,  and  in  fact,  the 
starting  torque  may  be  made  nearly  equal  to  that  of  a  squirrel- 
cage  induction  motor.  To  obtain  the  greatest  possible  start- 
ing torque,  the  squirrel-cage  winding  or  the  grids  employed, 
must  be  made  of  high  resistance.  On  the  other  hand,  to  secure 
the  greatest  damping  effect  so  as  to  prevent  hunting,  the  resist- 
ance must  be  kept  low.  The  two  requirements  are  therefore 
opposed  to  one  another,  and  the  designer  must  exercise  his 
judgment  as  to  the  best  average  solution. 

In  starting  in  this  way,  the  machine  will  accelerate  until  it 
is  nearly  in  synchronism,  or  if  the  load  is  light  may  attain  full 
synchronism.  This  latter  is  due  to  the  fact  that  the  " poles" 
of  the  armature  attract  strongly  those  of  the  field,  and  since 
the  relative  motion  is  small  near  synchronism,  they  are  fre- 
quently able  to  exert  enough  pull  to  bring  the  field  up  to 
full  synchronism.  Having  once  attained  this  speed,  the  pull 
is  easily  sufficient  to  retain  the  field  at  full  synchronism.  In 
any  event,  as  soon  as  the  field  current  is  applied,  the  attraction 
becomes  sufficiently  strong  so  that  the  field  is  pulled  into  full 
synchronism,  and  the  machine  continues  to  operate  as  a  syn- 
chronous motor. 

In  many  cases  it  is  desirable  to  construct  a  synchronous  motor 
with  laminated  .poles  instead  of  solid  ones.  Such  a  motor  will 
also  exert  a  moderate  starting  torque.  This  is  due  to  hysteresis 


SYNCHRONOUS  GENERATORS  AND  MOTORS  233 

and  eddy  current  loss  in  the  field  poles.  As  is  explained  under 
induction  motors  (see  Art.  251),  any  loss  in  the  rotor  causes  a 
torque.  Since  the  laminations  are  usually  rather  thick,  causing 
a  large  eddy  current  loss,  and  since  the  flux  densities  when  operat- 
ing in  this  manner  are  large  (giving  a  large  hysteresis  loss), 
the  torque  developed  may  be  considerable.  Of  course,  in  most 
motors  both  of  these  actions  are  present  to  some  extent. 

In  starting  up  a  synchronous  motor  in  this  manner,  the  field 
is  either  left  open  or  is  closed  through  a  resistor.  As  the  flux  set 
up  by  the  current  in  the  armature  rotates  rapidly  around  the 
stationary  field,  there  is  a  change  of  flux  through  the  field  wind- 
ings of  the  frequency  of  the  applied  current.  Thus,  at  one 
instant  a  north  "pole"  of  the  armature  will  be  opposite  one  of 
the  field  poles,  and  flux  will  be  passing  into  the  field  pole.  An 
instant  later,  a  south  "pole"  will  be  opposite  this  "field  pole 
and  the  flux  through  it  will  be  reversed.  This  rapid  reversal  of 
the  flux  induces  an  e.m.f.  in  the  field  winding,  and  since  the 
number  of  turns  in  the  field  winding  is  large  and  all  these  turns 
are  connected  in  series,  the  induced  voltage  will  generally  be 
high.  In  a  moderate-sized  machine,  this  may  readily  amount 
to  several  thousand  volts;  the  use  of  a  resistor  connected  across 
the  field  terminals  greatly  reduces  this.  As  the  field  begins  to 
rotate,  this  voltage  becomes  less,  since  the  cutting  is  less  rapid, 
and  at  exact  synchronism  the  induced  e.m.f.  is  zero,  since  the 
flux  and  the  field  are  moving  at  the  same  speed. 

In  addition  to  the  danger  to  life  from  this  high  voltage,  there 
is  also  danger  that  the  insulation  of  the  field  may  be  punctured. 
To  guard  against  this,  it  is  necessary  that  the  insulation  of  the 
field  be  much  thicker  than  would  be  necessary  if  the  machine 
were  not  to  be  started  in  this  manner.  Synchronous  converters 
(which  operate  as  synchronous  motors  as  long  as  no  continuous 
current  is  taken  from  them)  are  also  often  started  in  this  way. 
In  this  case,  since  the  field  is  stationary,  it  is  possible  to  avoid 
this  high  voltage  to  some  extent  by  disconnecting  the  field  coils 
from  one  another,  thus  reducing  the  induced  voltage  since  the 
sections  are  no  longer  connected  in  series.  A  switch  for  this 
purpose  is  known  as  a  field  break-up  switch. 

218.  Combination  Methods  of  Starting. — In  many  cases  in 
practice,  a  combination  of  some  of  the  preceding  methods  of 
starting  may  be  advisable.  Thus  it  sometimes .  occurs  in  the 
operation  of  motor-generator  sets  or  of  synchronous  converters 


234    j'jti \ciri. KX  w  DYXAMO  KLKCTRIC  MACHINERY 

that  starting  from  the  continuous-current  side  is  difficult  on 
account  of  fluctuations  in  the  supply  voltage.  This  variation 
may  introduce  danger,  since  the  voltage  may  change  just  as  the 
operator  is  starting  to  throw  the  switch,  or  it  may  be  that  a  great 
amount  of  time  is  necessary  to  secure  proper  conditions  for 
synchronizing.  This  is  very  objectionable,  particularly  in  the 
case  of  rotaries  or  motor-generator  sets  supplying  current  to 
electric  railways.  The  difficulty  may  be  avoided  by  running  the 
machine  up  to  a  speed  considerably  above  synchronism  by  means 
of  the  continuous  current  and  then  disconnecting  the  machine 
from  the  direct-current  line.  The  operator  then  watches  the 
synchronism  indicator  until  the  speed  has  fallen  nearly  to 
synchronism.  The  field  of  the  synchronous  machine  is  opened 
and  the  machine  connected  to  the  alternating-current  line. 
The  field  circuit  is  immediately  closed  again  and  the  machine 
drops  into  step.  The  disturbance  to  the  line  voltage  is  less  in 
amount  and  lasts  for  a  much  shorter  time  than  would  be  the  case 
if  the  machine  were  started  entirely  by  means  of  the  alternating 
current.  At  the  same  time,  the  skill  and  attention  required 
of  the  operator  is  much  less  than  would  be  the  case  if  the  machines 
were  synchronized,  since  the  machine  being  started  need  be  only 
approximately  at  synchronous  speed.  If  thrown  directly  on 
the  line,  a  synchronous  motor  takes  from  four  to  eight  times 
full-load  current.  This  is  undesirable  since  the  current,  in  addi- 
tion to  being  large,  also  lags  nearly  90°  and  generally  seriously 
lowers  the  voltage  of  the  line.  Any  of  the  starting  devices  used 
with  induction  motors  may  be  used  to  reduce  the  starting  current. 
A  synchronous  motor  is,  however,  often  supplied  from  its  own 
transformers,  and  a  rotary  converter  is  almost  always  so  supplied. 
In  such  cases  the  cheapest  starting  arrangement  is  the  use  of  low- 
voltage  taps  from  the  transformers  in  connection  with  a  double- 
throw  switch.  For  further  information  in  regard  to  starting 
devices,  see  the  section  on  induction  motors  (Art.  262.) 

219.  Armature  Reaction. — So  far  in  the  discussion  of  the 
synchronous  machine  the  magnetizing  effect  of  the  armature 
current  has  been  neglected.  In  Fig.  159  if  the  point  marked  N 
on  the  armature  be  considered,  it  will  be  seen  that  all  of  the 
currents  to  the  right  of  this  point,  for  a  distance  equal  to  the  pole 
pitch,  are  in  the  one  direction,  while  those  on  the  other  side  flow 
in  the  opposite  direction.  This  portion  of  the  armature  surface 
then  has  currents  circulating  around  it,  and  a  tendency  will  exist 


SYNCHRONOUS  GENERATORS  AND  MOTORS  235 

to  form  a  pole  there.  If  the  machine  is  operating  as  a  generator, 
the  polarity  of  the  armature  will  be  as  shown.  This  is  necessary 
if  the  machine  is  to  develop  power,  as  the  poles  of  the 
armature  may  be  regarded  as  attracting  those  of  the  field.  This 
is  perhaps  not  as  exact  a  method  of  looking  at  the  subject  as  that 
formerly  used,  but  it  is  occasionally  very  useful,  as  in  the  present 
instance.  If  the  machine  is  operating  as  a  motor,  the  polarity 
of  the  armature  will  of  course  be  reversed. 

The  diagram  shown  is  that  for  unity  power  factor.  Whether 
the  action  is  that  of  a  generator  or  a  motor,  the  magnetizing 
action  will  be  weak.  This  arises  from  the  fact  that  the  points  of 
greatest  magnetic  action  of  the  armature  are  situated  half  way 
between  the  field  poles,  and  hence  have  comparatively  little 
effect  upon  them.  There  is,  however,  a  tendency  to  distort  the 
flux,  causing  it  to  be  strengthened  in  one  pole  tip  and  weakened 
in  the  other. 

If  the  current  is  either  leading  or  lagging  by  90°,  the  conditions 
are  the  best  for  the  armature  to  exert  a  strong  magnetic  action 
upon  the  field.  At  smaller  angles  of  lag  or  lead  the  current  will 
have  a  smaller  magnetizing  or  demagnetizing  effect.  Thus  in 
Fig.  163,  in  which  the  current  of  a  generator  is  lagging  by  about 
40°,  it  will  be  seen  that  the  poles  of  the  armature  are  partially 
over  those  of  the  field  of  the  same  polarity.  Thus  a  leading 
current  in  a  motor  or  a  lagging  current  in  a  generator  exerts  a 
strong  demagnetizing  action.  Conversely,  a  lagging  current  in  a 
motor  or  a  leading  current  in  a  generator  tends  to  increase  the 
magnetization. 

220.  Regulation. — It  results  from  the  foregoing  facts  that  the 
regulation  of  an  alternating-current  generator  is  more  dependent 
upon  the  nature  of  the  load  than  is  that  of  a  continuous-current 
machine.  In  the  latter  the  only  variable  is  the  current;  in  the 
former  we  have  to  consider  both  the  current  and  its  angle  of 
lag  or  lead.  In  Fig.  181,  the  middle  curve  represents  the  varia- 
tion of  the  voltage  of  an  alternating-current  generator  with 
current  output,  the  speed  and  field  current  being  constant,  for 
100  per  cent,  power  factor.  The  voltage  drops  off  as  the  load  is 
increased,  the  curve  being  approximately  the  same  as  would  be 
obtained  in  the  case  of  a  separately  excited  continuous-current 
generator.  If,  however,  the  current  is  lagging,  the  voltage  will 
drop  off  much  more  rapidly,  as  shown  in  the  lower  curve  of  the 
same  figure.  If,  on  the  contrary,  the  current  is  leading,  the 


230      PRINCIPLE*  OF  DYNAMO  ELECTRIC  MACHINERY 

voltage  will  drop  less  or  even  rise  as  the  current  increases.     This 
is  indicated  in  the  upper  curve  of  Fig.  181. 

This  peculiar  behavior  of  the  synchronous  generator  is  due  to 
the  magnetic  action  of  the  armature  as  just  described.  If  the 
machine  is  furnishing  a  lagging  current,  there  is,  in  addition  to  the 
drop  in  the  armature  due  to  resistance  and  the  drop  due  to  react- 
ance, a  large  reduction  of  the  useful  magnetic  flux  of  the  machine 
due  to  the  demagnetizing  action  of  the  armature.  This  also 
reduces  the  voltage.  If,  on  the  other  hand,  the  current  is  leading, 
the  armature  tends  to  magnetize  the  field  and  the  external  volt- 
age is  increased. 


25 


50  75  100 

Amperes  in  Armature 

FIG.  181. 

In  giving  the  regulation  of  an  alternator,  it  is  necessary  that 
the  power  factor  be  stated.  Thus,  a  machine  which  has  a  regula- 
tion of  6  per  cent,  at  100  per  cent,  power  factor  will  have  a  regula- 
tion of  perhaps  20  per  cent,  at  80  per  cent,  power  factor  lagging 
current,  and  perhaps  one  of  —5  per  cent,  at  80  per  cent,  power 
factor  leading  current. 

221.  Rating  of  Synchronous  Machine. — We  must  also  keep 
these  facts  in  mind  in  stating  the  rating  of  a  machine.  An 
alternator  is  rated  usually  in  kilovolt-amperes,  i.e.,  it  is  rated 
to  deliver  a  certain  voltage  and  a  certain  amperage.  The  power 
will  be  the  same  as  the  kv-a.  in  case  the  power  factor  is  unity. 
At  any  other  power  factor  the  power  will  be  reduced  in  the  same 
proportion  as  the  power  factor.  Moreover,  with  low  power  factor 
and  lagging  current  it  is  necessary  that  the  field  be  far  stronger 
than  normal.  We  could,  for  example,  hardly  expect  an  alternator 
to  carry  its  full  kv-a.  rating  at  a  power  factor  of  zero  lagging 


SYNCHRONOUS  GENERATORS  AND  MOTORS  237 

current,  since  an  unreasonably  strong  field  would  be  required. 
In  case  the  generator  must  cope  with  unusual  conditions,  the 
requirements  should  be  clearly  stated  in  the.  specifications. 

This  peculiarity  of  the  regulation  of  the  alternating-current 
generator  makes  it  difficult  to  devise  any  system  of  compounding 
which  will  be  suitable  under  all  circumstances.  Formerly,  when 
alternators  were  used  almost  exclusively  on  lighting  loads  having 
a  power  factor  of  nearly  100  per  cent.,  alternators  were  frequently 
compounded  in  nearly  the  same  manner  as  continuous-current 
machines.  The  alternators  were  built  with  stationary  fields  and 
revolving  armatures,  and  a  commutator  was  added  to  rectify  the 
alternating  current  as  it  passed  through  the  series  field.  In 
many  cases,  instead  of  rectifying  the  actual  current  of  the  machine, 
a  current  transformer  was  used,  and  the  current  from  the  second- 
ary of  this  was  rectified.  However,  this  compounding  or 
compensating,  as  it  was  more  commonly  called,  was  ordinarily 
correct  only  for  a  non-inductive  load.  With  a  lagging  current 
it  helped  a  little,  but  with  a  leading  current  it  was  worse  than 
useless.  Moreover,  it  was  necessary  to  set  the  brushes  in  such  a 
position  with  respect  to  the  commutator  that  the  brush  passed 
from  one  segment  to  the  next,  as  the  current  passed  through  its 
zero  value.  Any  change  in  the  lag  or  lead  of  the  current  caused 
this  point  to  change,  and  hence  led  to  sparking  unless  the  brushes 
were  shifted.  These  facts  have  caused  the  abandonment  of  this 
device,  and  at  the  present  time  practically  all  synchronous 
machines  are  built  with  revolving  fields  and  without  compensating 
windings.  Hand  regulation  is  generally  depended  upon,  or  in 
the  case  of  rapidly  fluctuating  loads,  some  one  of  the  various 
forms  of  automatic  regulators  is  employed. 

222.  Regulation  in  Large  Machines. — To  secure  good  regula- 
tion of  a  synchronous  machine  whether  used  as  a  generator  or  as 
a  motor,  it  is  necessary  that  the  magnetic  strength  of  the  field  be 
large  compared  with  that  of  the  armature.  In  order  that  the 
large  number  of  ampere  turns  on  the  field  should  not  force  too 
much  flux  across  the  air  gap  and  through  the  armature,  it  is  in 
turn  necessary  that  the  air  gap  be  large.  Thus  it  sometimes 
happens  that  in  the  case  of  large  turbo-alternators  with  few  poles 
the  air  gap  is  as  long  as  2J^  in.  A  small  fraction  of  this  would  be 
sufficient  as  far  as  mechanical  clearance  is  concerned. 

Good  regulation  is  almost  always  desirable  in  a  synchronous 
generator  in  the  smaller  sizes.  In  machines  of  large  size,  very 


238      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

good  regulation  is  not  always  advisable.  One  reason  for  this  is 
that  such  machines  are  used  in  power  houses  of  large  capacity, 
and  on  such  systems  the  load  is  not  liable  to  as  violent  fluctua- 
tions as  is  the  case  with  smaller  systems.  Moreover,  with  large 
machines  the  chance  of  injury  in  case  of  a  short-circuit  is  greater 
than  in  that  of  small  alternators.  A  machine  of  poor  regulation, 
particularly  if  the  regulation  is  relatively  poorer  in  the  case  of 
inductive  loads,  will  have  a  smaller  short-circuit  current  than 
would  one  of  good  regulation,  and  hence  would  be  less  liable  to 
suffer  damage  itself  or  to  injure  the  circuit-breakers  in  the  event 
of  a  short-circuit. 

223.  Effect  of  Good  Regulation  in  the  Synchronous  Motor. — 
With  the  synchronous   motor   the  case  is  somewhat  different. 
If  a  machine  has  good  regulation,  it  is  evident  that  if  the  adjust- 
ment of  the  field  current  is  somewhat  faulty,  the  machine  will 
take  a  large  leading  or  lagging  current.     Moreover,  a  drop  in  the 
line  voltage  will  have  the  same  effect  as  an  increase  in  the  field 
strength  and  vice  versa,  and  hence  will  lead  to  the  circulation  of  a 
large    current  through  the  machine.     This  increases  the  heat- 
ing, thus  cutting  down  the  capacity  of    the  machine,  and  at 
the  same  time  causes  it  to  operate  less  efficiently  since  the  copper 
loss    will   be   increased.     Hence,    from   the   standpoint    of   the 
operator  of  the  machine,  very  good  regulation  in  a  synchronous 
motor  is  not  desirable. 

From  the  standpoint  of  the  electricity  supply  company, 
however,  the  reverse  is  true.  If  for  any  reason  the  supply 
voltage  drops,  the  machine  takes  a  leading  current,  since  now  its 
voltage  is  higher  than  that  of  the  line.  A  leading  current  through 
an  inductive  line  has  the  effect  of  increasing  the  voltage  at  the 
end  of  the  line.  Hence  the  presence  of  the  synchronous  motor 
tends  to  prevent  the  fall  of  voltage.  The  reverse  action  takes 
place  in  the  event  of  a  rise  in  voltage.  A  simple  way  of  looking 
at  the  matter  is  to  regard  the  synchronous  machine  (whether  it  is 
acting  as  a  generator  or  as  a  motor)  as  a  sort  of  flexible  prop, 
tending  to  prevent  any  change  in  the  voltage  at  the  point  to 
which  it  is  applied.  This  corrective  action  will  be  more  effec- 
tive the  better  the  regulation  of  the  synchronous  machine,  and 
hence  good  regulation  in  motors  as  well  as  in  generators  is  de- 
sirable from  the  standpoint  of  the  power  company. 

224.  Synchronous  Condensers. — So  desirable  is  this  action, 
that  synchronous  machines  are  sometimes  installed  by  power 


SYNCHRONOUS  GENERATORS  AND  MOTORS  239 

supply  companies  for  the  sake  of  their  regulating  action  alone, 
or  they  may  be  utilized  to  carry  a  load  either  as  motors  or 
possibly  as  generators  in  addition.  However,  the  action  is  dif- 
ferent from  that  of  a  condenser.  The  latter  takes  a  leading 
current,  under  all  conditions.  The  synchronous  machine,  on 
the  other  hand,  takes  either  a  leading  or  a  lagging  current  as 
the  case  may  require,  the  current  in  each  case  being  such  as 
will  nearly  correct  the  departure  of  the  line  voltage  from  normal. 
In  other  cases  where  the  need  of  such  correction  is  not  press- 
ing enough  to  warrant  the  installation  of  a  synchronous  machine 
for  the  sole  purpose  of  keeping  the  voltage  constant,  it,  neverthe- 
less, is  worth  while  for  the  power  company  to  offer  a  better  rate 
to  a  large  customer  if  he  will  install  a  synchronous  motor  in- 
stead of  an  induction  motor.  In  many  cases,  the  contract 
specifies  that  the  field  current  of  the  synchronous  machine  shall 
be  adjusted  in  accordance  with  the  instructions  of  the  power 
company.  If  desirable,  the  field  may  be  so  strengthened  that 
the  machine  takes  a  leading  current,  thus  offsetting  lagging 
current  due  to  induction  motors  or  other  devices. 

PROBLEMS 

91.  A  certain  large  factory  is  equipped  with  induction  motors.     The 
input  to  the  factory  is  1000  kw.  at  a  power  factor  of  0.80,  the  current 
being  lagging.     It  is  proposed  to  install  a  synchronous  machine  running 
light  on  the  line  to  improve  this  power  factor  by  taking  a  leading  current. 
What  will  be  the  kv-a.  rating  of  the  synchronous  machine  if  the  power  factor 
is  raised  to  100  per  cent.?     If  to  90  per  cent.? 

92.  In  the  foregoing  factory  a  motor  is  needed  to  develop  1000  hp.     Assum- 
ing that  it  would  operate  as  a  motor  at  an  efficiency  of  90  per  cent.,  what 
would  be  the  kv-a.  rating  of  a  synchronous  machine  to  raise  the  power  factor 
to  unity  and  at  the  same  time  carry  1000  hp.  as  a  motor? 

93.  The  cost  of  motors  and  generators  increases  approximately  in  pro- 
portion to  the  square  root  of  the  capacity,  the  speed,  etc.,  being  the  same. 
What  would  be  the  relative  costs  of  the  two  machines  in  the  above  problems? 

94.  A  certain  power  house  is  equipped  with  ten  turbine-driven  alternators. 
The  rated  output  of  each  turbine  is  14,000  hp.     What  would  be  the  correct 
size  of  each  generator  to  utilize  the  full  power  of  the  turbines  if  it  is  as- 
sumed that  the  station  will  operate  at  100  per  cent,  power  factor?     What 
at  85  per  cent,  power  factor?     The  efficiency  of  the  generators  may  be 
taken  as  being  95  per  cent. 

95.  A  certain  station  operates  at  a  power  factor  of  65  per  cent,  and  has  a 
maximum  output  of  50,000  kw.     What  is  the  capacity  of  the  transformers 
required?     What  is  the  capacity  of  the  generators,  assuming  that  the  trans- 


240      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

former  efficiency  is  98  per  cent.?     What  is  the  horse-power  rating  of  the 
turbines,  assuming  a  generator  efficiency  of  95  per  cent.? 

96.  A  certain  alternator  is  operating  under  full  load  at  unity  power  factor 
and  a  terminal  voltage  of  4400.  When  the  load  is  reduced  to  zero,  the  speed 
and  the  field  excitation  being  kept  the  same,  the  voltage  increases  to  4730 
volts.  What  is  the  regulation  for  100  per  cent,  power  factor? 


CHAPTER  XVII 


THE    ROTARY    CONVERTER    OR    SYNCHRONOUS 
CONVERTER 

225.  General  Description. — A    rotary  converter   (frequently 
called  a  rotary)  is  intended  primarily  as  a  means  of  transforming 
alternating  to  continuous  current  or  vice  versa.     It  consists  essen- 
tially of  a  continuous-current  machine  to  which  two  or  more  slip 
rings  have  been  added.     These  rings  are  mounted  on  the  shaft 
and  connected  to  proper  points  in  the  armature  winding,  or  what 
is  equivalent,  to  proper  commutator  bars.     Suitable  brushes  are 
provided  to  carry  the  current 

from  the  rings  to  the  exter- 
nal circuit. 

Figure  182  shows  a  two- 
ring  or  single-phase  rotary. 
Without  the  slip  rings,  it 
would  be  a  continuous-cur- 
rent generator  or  motor. 
The  winding  is  shown  as  a 
ring  winding  merely  for  con- 
venience. In  practice,  drum 
windings  are  used  exclusively. 
Only  the  one  winding  is  used 
on  the  armature.  If  the  con-  FIG.  182. 

tinuous-current  brushes  were 

removed,  and  the  field  were  excited  in  some  suitable  manner, 
the  machine  would  operate  as  a  single-phase  alternating-current 
generator.  The  voltage  would  be  a  maximum  when  the  points 
connected  to  the  slip  rings  were  under  the  direct-current  brushes, 
and  at  that  time  would  be  equal  to  the  direct  e.m.f.  The  alter- 
nating voltage  would  be  zero  when  the  tapping  points  were  90 
electrical  degrees  from  the  above  position.  It  is  also  evident 
that  the  machine  would  operate  as  a  single-phase  synchronous 
motor. 

226.  General  Operation. — If  the  machine  is  driven  by  external 
power  with  the  direct-current  brushes  on,  it  will  be  capable  of 

16  241 


242      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

operating  either  as  a  continuous-current  or  as  an  alternating-cur- 
rent generator.  It  is  also  possible  to  combine  these  functions 
and  use  the  machine  to  generate  both  kinds  of  current  at  the 
same  time.  The  machine  is  then  known  as  a  double-current 
generator.  Machines  are  occasionally  used  in  this  manner  to 
furnish  continuous  current  to  a  trolley  line  in  the  vicinity  of  the 
station.  The  current  for  the  distant  parts  of  the  line  is  taken 
out  as  alternating  current.  This  is  then  stepped  up  in  trans- 
formers, transmitted  over  the  high-tension  lines,  stepped  down 
to  the  proper  voltage,  and  transformed  into  continuous  current 
by  means  of  rotary  converters. 

It  will  also  be  apparent  that  if  the  machine  is  operated  as  a 
continuous-current  motor,  there  will  be  present  at  the  slip 
rings  an  alternating  e.m.f.  It  is  therefore  possible  to  take 
alternating  current  from  these  rings.  The  machine  is  then 
operating  to  change  continuous  current  into  alternating.  When 
used  in  this  manner,  it  is  called  an  inverted  rotary.  This  use 
is  comparatively  infrequent. 

The  most  common  use  of  the  machine  is  to  convert  alter- 
nating current  into  continuous  current.  It  will  be  evident 
that  the  rotary  will  operate  as  a  synchronous  motor.  When 
running  in  this  manner,  there  is  a  constant  e.m.f.  at  the  direct- 
current  brushes,  and  by  connecting  to  a  suitable  receiving 
circuit,  continuous  current  can  be  led  off  and  utilized. 

227.  Field    Winding. — A   rotary   converter   may   be   excited 
by  any  of  the  methods  used  with  continuous-current  machines, 
Separate  excitation  is  frequently  used  in  the  case  of  inverted 
rotaries  for  a  reason  which  will  be  explained  presently.     Series 
excitation    is    rarely,  if  ever,   employed.     Shunt   excitation   is 
common  with  rotaries  used  on  lighting  circuits,  while  those  em- 
ployed in  connection  with  railroad  work  are  usually  compounded. 

228.  Voltage  Relations. — As  was  pointed  out,  in  a  two-ring 
rotary  the  maximum  of   the  alternating-current  voltage  is  the 
same  as  the  continuous-current  voltage.     If  the  wave  shape  of 
the  alternating-current  voltage  is  sinusoidal,  the  effective  value 
of  the  alternating  voltage  will  be  equal  to  the  continuous  volt- 
age divided  by    \/2  or  equal  to  the  continuous  voltage  multi- 
plied   by    0.707.     Further,    if    four    rings    connected    to    four 
equidistant  points,  or  six  rings  connected  in  the  same  manner 
were  used,  the  voltage  across  any  diameter  would  be  given  by 
the  same  relation. 


THE  ROTARY  CONVERTER 


243 


The  three-phase  relation  is  somewhat  different.  Referring 
to  Fig.  183,  a  two-ring  or  single-phase  rotary  would  be  con- 
nected to  the  points  A  and  B.  The  circle  is  supposed  to  repre- 
sent a  ring  winding  of  the  kind  shown  in  Fig.  182.  A  four-ring 
or  so-called  two-phase  rotary  would  have  taps  at  the  points  A 
and  B,  and  C  and  D.  For  a  three-phase  winding  the  points  A, 
E,  and  F  would  be  used.  The  angle  EAB  is  equal  to  30°,  and 
we  have  the  relation 


AE  =  AB  cos  30°  = 


AB  =  0.8QQAB 


Also  since  A  B  is  equal  to  0.707  times  the  continuous  voltage, 

we  may  conclude  that  the  three-phase 

alternating  voltage  is  equal  to  0.707  X 

0.866  =  0.612     times     the     continuous 

voltage. 

The  six-phase  or  six-ring  connection 
is  sometimes  used  with  large  rotaries. 
This  would  require  connection  to  the 
points  AGEBFH.  The  voltage  across 
any  diameter  is  the  same  as  with  the 
single-phase  or  the  two-phase  connec- 
tion. 

229.  Starting. — In  general,  the  methods  of  starting  rotaries 
are  the  same  as  those  discussed  under  the  head  of  synchronous 
motors.  Any  of  the  methods  there  described  may  be  used.  On 
account  of  the  fact  that  rotaries  are  started  without  load,  and 
since  the  machines  are  small  for  their  rating,  starting  does  not 
present  as  great  difficulties  as  in  the  case  of  synchronous  motors. 

If  continuous  current  at  a  steady  voltage  were  always  present, 
starting  from  the  continuous-current  end  would  be  the  preferable 
method:  This  is,  however,  rarely  the  case.  Sometimes  a 
small  induction  motor  is  provided,  mounted  upon  the  end  of 
the  rotary  shaft.  This  motor  should  have  two  poles  less  than 
the  rotary  in  order  that  the  latter  may  be  brought  above  syn- 
chronous speed. 

If  the  rotary  is  to  be  started  from  the  alternating-current 
end,  it  is  customary  to  provide  the  fields  with  a  field  break-up 
switch,  to  avoid  danger  from  the  high  potential  generated  in 
the  field  when  the  machine  starts.  This  is  readily  done  since  the 
field  is  stationary. 


244      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

The  fact  that  the  rotary  converter  has  a  commutator,  leads  to 
a  little  difficulty  when  it  is  started  by  applying  current  to  the 
alternating-current  end.  At  least  one  armature  coil  for  each 
field  pole  is  short-circuited  by  the  brushes.  As  the  rotating 
field  revolves  around  the  armature  it  cuts  this  coil  and  generates 
a  large  current  in  it.  This  sometimes  causes  flashing  at  the 
brushes.  This  is  particularly  true  in  the  case  of  commutating 
pole  rotaries.  In  these  machines  it  is  usually  necessary  to  pro- 
vide means  for  raising  the  direct-current  brushes  while  the  ma- 
chine is  being  started. 

230.  Reversed  Polarity  at  Start. — One  point  in  which  the  opera- 
tion is  different  from  that  of  a  motor-generator  set  (that  is,  an 
alternating-current  motor  driving  a  direct-current  generator) 
deserves  mention.  In  the  latter,  the  direct-current  machine 
acts  like  any  other  generator  and  will  always  build  up  with 
the  same  polarity,  unless  something  out  of  the  ordinary  has 
happened  to  reverse  it.  In  the  rotary,  however,  it  will  be 
apparent  that  when  the  armature  is  at  rest  and  an  alternating 
current  is  passed  into  the  slip  rings,  there  will  be  an  alternating 
potential  at  the  continuous-current  brushes.  The  frequency 
will  be  the  same  as  that  of  the  supply.  This  is  due  to  the  rotary 
magnetic  field  set  up  around  the  armature  by  the  action  of  the 
alternating  current.  As  the  armature  starts  to  rotate  it  moves 
in  the  opposite  direction  to  this  rotating  magnetic  field,  and  as 
the  motion  of  the  latter  is  relative  to  the  armature  surface, 
its  speed  of  rotation  becomes  less.  At  full  synchronism  this 
rotating  magnetic  'field  is  stationary  with  respect  to  the  field 
and  brushes.  The  frequency  of  the  alternating  e.m.f.  at  the 
direct-current  brushes  therefore  becomes  less  as  the  armature 
approaches  synchronism. 

A  direct-current  voltmeter  connected  to  the  continuous-current 
brushes  will  at  first  give  no  indication  when  the  machine  is  at- 
tached to  the  alternating-current  mains,  since  the  alternating 
potential  is  of  too  high  a  frequency  to  affect  it.  As  the  armature 
gains  speed  the  needle  will  at  first  tremble,  then  begin  to  swing 
across  the  scale,  first  in  one  direction  and  then  in  the  other. 
If  the  applied  e.m.f.  is  sufficiently  high,  the  machine  may  pull 
into  complete  synchronism  before  there  is  any  current  in  the 
field.  In  this  event,  the  deflection  of  the  needle  will  become 
steady.  This  permanent  deflection  may  be  in  either  of  the 
two  directions.  Whether  the  deflection  is  positive  or  negative 


THE  ROTARY  CONVERTER  245 

depends  upon  whether  a  north  pole  of  the  armature  takes  hold 
of  what  would  normally  be  a  north  pole  of  the  field,  or  the  re- 
verse. No  matter  what  the  potential  of  the  brushes  when  the 
machine  falls  into  synchronism,  if  the  field  circuit  be  closed  the 
machine  will  excite  itself  and  continue  to  operate.  This  is  in 
consequence  of  the  fact  that  a  continuous-current  machine  can 
excite  itself  in  either  direction. 

It  is  of  course  essential,  in  general,  that  the  machine  excite 
itself  in  the  usual  direction  before  it  is  thrown  on  the  load.  If 
the  attendant  watches  carefully  as  the  machine  approaches  syn- 
chronism, and  closes  the  field  switch  just  as  the  voltmeter  is 
starting  a  positive  swing,  the  machine  will  build  up  in  the  proper 
manner.  If  a  failure  should  be  made  in  this,  the  field  switch 
and  then  the  main  switch  may  be  opened  for  an  instant  to  allow 
the  machine  to  drop  out  of  step,  and  a  new  attempt  may  be 
made. 

This  is  sometimes  objectionable  since  it  causes  a  sudden  rise 
in  voltage  followed  by  a  fall.  Moreover  it  is  necessary  to  break 
the  large  alternating  current,  thus  causing  considerable  burning 
of  the  switch.  It  is  perhaps  better  to  provide  a  switch  which 
will  reverse  the  connections  of  the  field  to  the  armature.  This 
has  the  effect  of  quickly  bringing  the  field  magnetism  down 
to  zero,  since  the  current  in  the  field  is  in  the  wrong  direction 
to  magnetize  it.  The  machine  will  then  drop  out  of  step  and 
by  quickly  reversing  the  switch  as  the  voltmeter  passes  through 
zero,  the  machine  can  be  brought  to  the  proper  condition  for 
operation.  The  voltage  of  the  machine  is  then  adjusted  to 
the  same  value  as  that  of  the  bus-bars,  and  the  main  switch 
thrown  in  the  same  manner  as  for  a  direct-current  machine. 

231.  Voltage  Control. — As  already  shown,  there  is  a  definite 
relation  between  the  voltage  of  the  alternating-  and  the  con- 
tinuous-current brushes  of  a  rotary  converter.  This  ratio  is 
somewhat  modified  by  the  drop  in  the  winding  when  the  machine 
is  delivering  current,  but  remains  practically  constant.  In 
order,  then,  to  be  able  to  vary  the  voltage  at  the .  continuous- 
current  brushes,  it  is  necessary  to  have  some  means  of  chang- 
ing the  voltage  at  the  alternating  end. 

The  first  thought  is  that  it  should  be  possible  to  regulate 
the  voltage  by  changing  the  field  current  in  the  same  manner  as 
in  the  case  of  a  direct-current  machine.  If,  however,  the  regula- 
tion of  the  supply  line  and  the  generators  is  such  that  the  al- 


246      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

ternating-current  voltage  is  really  constant,  this  would  have  no 
effect.  The  result  would  be  that  the  machine  would  draw  a 
large  current,  leading  if  the  field  were  strong  and  lagging  if  it 
were  weak,  and  this  current  would  demagnetize  or  magnetize 
the  field  so  as  to  produce  substantially  the  same  generated 
alternating  voltage.  This  matter  has  been  fully  treated  in 
connection  with  synchronous  machines.  (See  Art.  206.)  A 
study  of  this  section  will  show  that  the  back  alternating  e.m.f. 
of  the  rotary  does  increase  somewhat  as  the  field  is  strengthened, 
but  only  to  a  minor  extent.  An  attempt  to  control  the  voltage 
in  this  way  would  therefore  have  little  effect  in  cases  where  the 
regulation  of  the  alternating  supply  voltage  is  good. 

In  practice,  however,  there  is  sure  to  be  more  or  less  resist- 
ance and  reactance  in  all  transmission  lines.  The  line  voltage 
therefore  acts  as  though  it  were  flexible  instead  of  rigid,  and 
allows  the  potential  at  the  receiving  end  to  be  adjusted  more  or 
less  independently  of  that  at  the  sending  end.  This  is  treated  in 
detail  in  Arts.  174-176.  It  is  shown  there  that  a  leading  current 
produced  by  a  strong  field  raises  the  voltage,  while  a  lagging 
current  with  weak  field  lowers  it.  In  many  cases  of  rotary 
converter  practice,  the  natural  reactance  of  the  line  is  insufficient, 
and  it  becomes  necessary  to  install  reactors  in  the  converter 
substation. 

When  this  method  of  control  is  adopted,  it  is  customary  to 
make  the  action  automatic  by  using  a  compound  winding  on  the 
rotary.  As  the  load  increases  the  flux  is  increased  by  the  action 
of  the  series  field,  the  machine  draws  a  leading  current,  and  the 
potential  at  the  alternating-current  rings  is  therefore  raised  or 
held  constant  according  to  the  adjustment  of  the  compounding 
and  the  reactance  of  the  line.  This  arrangement  of  the  apparatus 
is  in  almost  universal  use  in  the  substations  of  electric  railway 
systems.  The  variations  of  load  are  so  frequent  that  it  would  be 
impracticable  to  attempt  to  follow  them  with  hand  regulation. 

Sight  should  not  be  lost  of  the  fact  that  by  operating  in  this 
way,  with  leading  or  lagging  current,  the  heating  of  the  rotary 
is  increased;  or  what  is  equivalent,  its  capacity  is  decreased 
since  operation  much  of  the  time  is  at  low  power  factor.  This  is 
not  always  a  serious  objection,  as  in  railway  work  the  rotary  is 
frequently  called  upon  to  carry  only  a  moderate  average  current, 
and  its  capacity  is  limited  more  by  considerations  of  its  possible 
overload  than  by  its  heating.  It  is  certain,  however,  that  the 


THE  ROTARY  CONVERTER  247 

combined  efficiency  of  both  the  line  and  of  the  rotary  is  lowered 
by  the  increased  current  they  are  called  upon  to  carry. 

232.  Use  of  Voltage  Regulators. — It  is  also  apparent  that 
the  alternating-  and,  consequently,  the  continuous-current  vol- 
tage of  a  rotary  could  be  changed  by  providing  a  number  of 
different  taps  giving  several  voltages  from  the  transformers. 
There  are  two  serious  objections  to  this  plan.  Rather  elaborate 
arrangements  would  have  to  be  made  to  avoid  breaking  the 
circuit  and  consequently  throwing  the  rotary  out  of  step  in 
passing  from  one  voltage  to  another.  Moreover,  the  number  of 
steps  would  need  to  be  very  large,  if  sufficiently  close  adjust- 
ment of  voltage  were  provided.  This  plan  is  consequently 
not  in  practical  use. 

The  most  common  method  of  varying  the  alternating- 
voltage  is  by  means  of  a  polyphase  potential  regulator.  Such 
a  machine  is  shown  in  Fig.  184.  The  mechanical  construction 
is  similar  to  that  of  an  induction  motor,  except  that  the  "rotor" 
is  incapable  of  rotation  except  through  a  comparatively  small 
angle.  This  movement  is  effected  by  means  of  a  worm  and 
wheel,  and  frequently  a  small  motor  is  provided  to  allow  the 
action  to  be  controlled  from  a  distance.  The  primary  is  con- 
nected across  the  line  (usually  three  phase)  while  the  secondary 
is  connected  in  series  with  it. 

It  is  clear  from  the  action  of  the  induction  motor  (see  Art. 
248)  that  a  rotating  magnetic  field  will  be  set  up  in  the  primary, 
and  since  the  applied  voltage  is  approximately  constant,  the  flux 
also  will  be  constant.  A  constant  voltage  will  then  be  in- 
duced in  the  secondary.  It  would  appear  that  a  constant 
voltage  would  then  be  added  to  the  primary  voltage  and  that 
there  would  be  no  possibility  of  regulation.  It  must  be  con- 
sidered, however,  that  as  the  secondary  is  turned,  the  phase 
angle  of  the  generated  voltage  with  respect  to  the  primary 
changes.  We  then  have  the  sum  of  two  constant  voltages 
but  the  angle  between  them  may  be  anything  desired.  The 
vector  sum  of  the  two  may  then  be  anything  from  the  arith- 
metical sum  to  the  arithmetical  difference  of  the  two.  If, 
therefore,  the  secondary  should  give  a  maximum  voltage  of  say 
50  volts,  it  would  be  possible  to  raise  or  lower  the  primary 
voltage  by  50  volts,  giving  a  range  of  regulation  of  100  volts. 

This  method  possesses  great  advantages.  As  noted,  the 
apparatus  can  readily  be  arranged  for  control  from  a  distance. 


248      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


The  changes  of  voltage  may  be  made  as  small  as  desirable,  and 
there  are  no  sudden  jumps  in  e.m.f.  With  any  given  alternating 
voltage,  the  field  current  of  the  rotary  may  be  so  adjusted  that 
the  power  factor  is  unity  and  consequently  the  rotary  and 
line  will  be  operating  at  their  best  efficiency.  This  method  of 
control  is  commonly  adopted  in  substations  on  large  lighting 
and  power  circuits  in  cities.  The  changes  of  load  are  gradual, 
and  there  is  usually  no  difficulty  in  taking  care  of  them  by  hand 
regulation: 


FIG.  184. 

Another  method  that  has  been  employed  to  some  extent  is  to 
provide  the  rotary  with  a  small  synchronous  machine  mounted 
on  the  rotary  shaft.  The  armature  windings  of  this  synchronous 
machine  are  connected  in  series  with  the  leads  of  the  rotary,  and 
the  field  excitation  is  so  arranged  that  any  value  of  the  field 
current  from  zero  to  a  maximum  in  either  direction  can  be 
readily  obtained.  The  synchronous  machine  is  mounted  on 
the  shaft  in  such  an  angular  relation  to  the  rotary  armature 
that  its  e.m.f.  is  either  in  phase  with  or  in  phase  opposition 
to  the  e.m.f.  of  the  rotary.  By  proper  manipulation  of  the 


THE  ROTARY  CONVERTER 


249 


field  rheostat  of  the  synchronous  machine,  any  desired  voltage 
within  the  range  of  the  auxiliary  machine  may  be  either  added 
to  or  subtracted  from  the  voltage  of  the  rotary.  Since  the 
voltage  of  the  line  remains  substantially  constant,  the  voltage 
of  the  rotary  will  vary.  The  action  may  be  made  automatic 
if  desired  by  compounding  the  field  of  the  auxiliary  machine 
with  the  continuous  current  delivered  by  the  rotary.  A  machine 
of  this  type  is  shown  in  Fig.  185. 


FIG.  185. 

233.  Split-pole  Rotaries. — The  type  of  machine  known  as  the 
split-pole  rotary  offers  many  advantages  over  any  other  form 
of  adjustable  voltage  rotary.  In  these,  each  of  the  usual  field 
poles  is  split  up  into  two  or  three  parts,  with  separate  windings. 
The  two-part  pole  is  the  more  common. 

It  has  been  pointed  out  that  the  maximum  voltage  at  the 
alternating-current  rings  is  the  same  as  the  steady  value  of  the 
continuous  voltage  in  the  case  of  a  two-ring  or  a  four- 
ring  rotary.  This  holds  true,  however,  only  when  the  con- 
tinuous-current brushes  are  on  the  neutral  point.  If  they  are 
moved  from  this  point,  the  continuous  voltage  becomes  less  than 
the  maximum  of  the  alternating  voltage.  It  would,  however, 


250      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


not  be  practicable  to  attempt  to  vary  the  direct  voltage  by  shifting 
the  brushes  since  the  sparking  would  be  prohibitive.  What  is 
done  is  to  keep  the  brushes  stationary  and  shift  the  field,  leaving 
a  neutral  space  at  the  position  of  the  conductors  undergoing 
commutation. 

An  outline  drawing  of  a  two-pole  rotary  embodying  these 
principles  is  shown  in  Fig.  186.  Connections  are  made  so  that 
the  current  around  the  poles  N'  and  S'  may  be  varied  in  strength 
and  may  be  passed  in  either  direction.  If  N'  and  S'  are  of  the 
polarity  shown  the  direct  voltage  will  be  lowered.  On  the  other 

hand,  it  will  be  raised  if  they 
are  reversed.  Changes  in  N' 
and  S',  however,  have  little 
effect  upon  the  alternating 
voltage  since  the  voltage  in- 
duced by  the  flux  from  N'  and 
S'  is  nearly  at  right  angles  to 
that  due  to  the  main  flux.  We 
may  therefore  obtain  a  wide 
range  of  direct  voltage  with 
but  little  change  in  the  alter- 
nating voltage.  The  distribu- 
tion of  the  flux  changes  some- 
what as  the  voltage  is  varied, 
and  the  wave  shape  of  the 

alternating  voltage  may  be  somewhat  changed.  This  may, 
however,  be  largely  avoided  by  proper  shaping  of  the  pole 
faces. 

It  is  desirable  that  the  wave  shape  be  distorted  as  little  as 
possible,  since  if  the  wave  shape  of  the  rotary  is  not  the  same  as 
that  of  the  circuit,  they  will  fail  to  balance  one  another  at  all 
times,  and  idle  currents  will  circulate  in  the  windings.  It  will 
then  be  impossible  to  adjust  the  rotary  to  unity  power  factor, 
since  additional  current  will  always  flow.  The  matter  is  not  one 
of  paramount  importance,  and  some  distortion  can  be  introduced 
without  serious  effect.  Some  split-pole  rotaries,  in  fact,  operate 
upon  this  principle.  Thus  if  we  change  from  a  flat-top  wave  to  a 
peaked  one  without  changing  the  effective  value  of  the  alternating 
voltage,  the  direct  voltage  will  in  both  cases  be  equal  to  the 
maximum  value  of  the  alternating  voltage,  and  consequently  it 
will  be  much  greater  with  the  peaked  wave. 


FIG.  185. 


THE  ROTARY  CONVERTER  251 

The  split-pole  rotary  is  a  desirable  piece  of  apparatus,  since 
it  combines  in  itself  all  the  elements  required  for  regulating  as 
well  as  for  converting  the  current.  The  cost  of  building  a 
machine  of  this  character  should  not  be  seriously  higher  than 
that  of  a  plain  rotary  and  presumably  would  be  less  than  that  of  a 
rotary  and  potential  regulator. 

234.  Heating  of  Rotary  Converters. — In  general,  the  heating 
of  a  rotary  converter  is  much  less  than  that  of  the  same  machine 
used  as  a  continuous-current  generator.  Referring  to  Fig.  182, 
it  will  be  seen  that  four  times  in  each  revolution  an  alternating- 
current  brush  is  connected  to  a  continuous-current  brush  and 
current  passes  directly  into  the  continuous- current  system  without 
passing  through  the  armature  winding.  If  the  taps  are  made  on 
the  back  of  the  armature,  the  current  passes  through  only  one 
conductor  at  these  times;  and  if  the  taps  are  connected  to  the 
commutator,  it  does  not  pass  through  any  winding.  If  the  rotary 
has  three  rings,  there  are  six  times  in  each  cycle  when  the  current 
can  pass  directly  from  one  system  to  the  other.  With  four  rings 
there  are  eight,  and  with  six  rings,  twelve  such  opportunities. 

On  the  other  hand,  in  the  case  of  the  two-ring  rotary  the  alter- 
nating current  is  41  per  cent,  larger  than  the  direct  current  of  a 
direct- current  machine  of  the  same  rating.  This  tends  to  increase 
the  heating  and  it  can  be  shown  that  it  is  more  than  sufficient 
to  offset  the  advantage  just  described,  particularly  in  the  coils 
close  to  the  tapping  points.  With  more  than  two  rings  (as  is 
practically  always  the  case  in  practice)  the  rotary  heats  less  than 
it  would  as  a  direct-current  generator  operating  at  the  same 
rating. 

In  accordance  with  these  facts,  rotaries  are  rated  higher  than 
the  same  machines  would  be  as  direct-current  generators.  The 
following  table  gives  the  relative  ratings: 

Direct-current  generator  100  per  cent. 

Two-ring    rotary 85  per  cent.     (Practically  never  used.) 

Three-ring  rotary 132  per  cent. 

Four-ring  rotary 162  per  cent. 

Six-ring   rotary 192  per  cent. 

The  foregoing  are  on  the  basis  of  unity  power  factors.  If  the 
adjustment  of  the  rotary  field  is  such  that  it  takes  a  current 
at  any  other  power  factor,  the  alternating  current  will  be  larger 
and  consequently  the  heating  will  be  greater.  The  designer 
would  therefore  hesitate  to  take  full  advantage  of  the  increased 


252      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

rating,  since  during  much  of  the  time,  the  rotary  will  be  operating 
at  other  than  unity  power  factor. 

235.  Commutation  of  Rotaries. — The  commutation  of  rotaries 
is  usually  good.     One  of  the  principal  causes  of  commutation 
trouble  with  continuous-current  generators  is  the  fact  that  as  the 
load  on  a  machine  is  increased,  the  armature  sets  up  a  cross 
magnetizing  effect,  tending  to  distort  the  flux.     The  conditions 
for  correct  commutation  are  therefore  interfered  with  and  the 
machine  tends  to  spark.     This  cross  flux  may  be  thought  of  as 
setting  up  poles  on  the  armature  at  points  approximately  midway 
between  the  field  poles. 

If  the  rotary  were  used  as  a  synchronous  motor,  there  would 
likewise  be  a  cross  flux  causing  poles  on  the  armature.  These 
would  be  midway  between  the  field  poles  if  the  machine  were 
operating  at  unity  power  factor.  The  poles  would,  however,  be 
of  the  opposite  sign  to  those  of  a  generator. 

When  the  rotary  is  in  normal  operation  converting  alternating 
to  continuous  current  or  vice  versa,  it  combines  the  functions  of  a 
continuous-current  generator  and  a  synchronous  motor.  It  will 
therefore  be  apparent  that  the  two  armature  fields  will  tend  to 
oppose  one  another,  and  the  net  result  will  be  a  small  field  of  the 
same  polarity  as  would  be  present  in  a  synchronous  motor.  There 
will  therefore  be  practically  no  distortion  of  the  magnetic  field 
as  the  load  comes  on,  and  consequently  there  will  be  but  little 
tendency  to  spark. 

If  a  rotary  hunts  there  is  alternately  a  strong  torque  tending  to 
accelerate  the  machine  and  to  retard  it.  To  produce  these 
torques,  requires  a  cross  magnetic  field,  first  in  the  one  direction 
and  then  in  the  other.  Under  these  conditions,  there  will  of 
course  be  a  decided  tendency  to  spark,  and  rotaries  sometimes 
flash  over  the  commutator  when  hunting.  The  pole  shoes, 
however,  are  frequently  provided  with  damping  grids  as  de- 
scribed' in  connection  with  synchronous  machines,  and  these  tend 
to  prevent  hunting.  Moreover  the  generators  supplying  current 
to  rotaries  are  usually  driven  by  rotating  prime  movers  such  as 
steam  or  water  turbines. 

236.  Frequency. — The  frequency  commonly  adopted  for  the 
operation  of  rotary  converters  is  25  cycles.     Sixty  cycle  rotaries 
are  in  use  to  a  large  extent  but  are  much  more  difficult  to  design, 
and  give  somewhat  less  satisfactory  results  in  operation.     A 
simple  calculation  will  suffice  to  show  the  difficulty.     Suppose  it 


THE  ROTARY  CONVERTER  253 

is  desired  to  design  a  60-cycle  rotary  for  electric  railway  work. 
The  rotary  would  be  required  to  generate  a  voltage  of  about  600 
volts  as  a  maximum.  It  is  found  that  in  order  to  obtain  satis- 
factory commutation,  it  is  desirable  that  the  average  voltage 
between  commutator  bars  should  not  exceed  15  volts.  This 
requires  forty  commutator  bars  between  neutral  points  on  the 
commutator.  This  holds  irrespective  of  the  number  of  poles  or 
the  type  of  winding  employed.  It  is  likewise  found  undesirable 
that  the  commutator  bars  be  made  less  than  y±  in.  in  width. 
The  distance  on  the  commutator,  from  one  neutral  point  to  the 
next,  must  then  be  at  least  J£  X  40  =  10  in.  Any  given  com- 
mutator bar  must  move  the  distance  from  one  neutral  point  to 
the  next  in  the  time  of  one-half  wave,  in  this  case  in  Jf  20  sec- 
The  surface  speed  of  the  commutator  must  then  be  !%2  X  120  X 
60  =  6000  ft.  per  minute.  This  is  over  a  mile  a  minute,  and  is 
an  undesirably  high  peripheral  speed.  The  conditions  for  a 
lower  voltage  would  be  nearly  as  bad,  as  it  would  not  be  prac- 
ticable to  use  so  high  an  average  value  of  the  volts  per  com- 
mutator bar.  The  difficulty  of  building  a  machine  for  this 
frequency  will  therefore  be  apparent.  These  difficulties  have, 
however,  been  largely  overcome  by  careful  design,  and  60-cycle 
rotaries  are  now  freely  used. 

237.  Connections  of  Rotaries. — There  are  a  great  variety  of 
possible  connections  of  rotaries.  In  the  following  figures,  the 
connections  of  the  secondaries  of  the  transformers  only  are  shown. 
The  primaries  might  be  connected  in  any  of  the  well-known  ways. 
Thus,  in  Fig.  187,  the  primary  connections  to  the  three-phase 
line  might  be  either  in  star  or  in  delta,  proper  provision  being 
made  in  the  former  case  to  hold  the  neutral  at  the  proper 
potential. 

In  Fig.  187,  the  secondaries  of  the  transformers  are  shown 
connected  in  Y  and  the  three  terminals  led  to  the  three  slip  rings 
of  the  rotary.  In  this  figure  the  two  continuous-current  brushes 
are  also  shown.  A  dotted  line  is  drawn  from  the  neutral  point  of 
the  transformers.  This  conductor  may  or  may  not  be  used. 
If  it  is  employed,  the  voltage  from  either  of  the  direct-current 
brushes  to  this  neutral  wire  will  be  half  of  the  generated  con- 
tinuous voltage.  This  wire  may  then  be  used  as  the  neutral  of  a 
three-wire  system. 

Figure  188  shows  a  three-phase  connection  in  which  the  sec- 
ondaries are  connected  in  delta.  In  this  case,  it  is  impossi- 


254      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


ble  to  have  a  neutral  wire  as  there  is  no  neutral  point  on  the 

transformers. 

As  previously  explained,  if  the  power  factor  is  at  or  near  unity, 

a  considerable  increase  in  the  out- 
put or  a  decrease  in  the  heating 
of  the  armature  of  a  rotary  results 
by  employing  six  rings  instead  of 
three.  The  rotary  is  then  known 


FIG.  187. 


FIG.  188. 


as  a  six-phase  or  six-ring  rotary.  The  six-phase  circuit  to  feed 
such  a  machine  is  readily  derived  from  the  secondaries  of  three 
transformers  connected  on  a  three-phase  circuit.  The  primaries 

of  fhe  transformers  .may  be 
connected  either  in  Y  or  in 
delta.  Instead  of  connecting 
the  secondaries  together,  they 


FIG.  189. 


FIG.  190. 


may  be  led  to  such  rings  that  the  ends  of  each  secondary  wind- 
ing are  connected  to  rings  connected  to  electrically  opposite 
points  of  the  armature  winding.  This  is  known  as  the  diametral 
connection  and  is  shown  in  Fig.  189.  The  neutral  points  of  the 


THE  ROTARY  CONVERTER 


255 


three  secondary  windings  may  be  connected  together  if  desired  as 
shown  by  the  dotted  line,  to  give  a  neutral  point. 

Figure  190  represents  the  six-phase  delta  connection.     To  use 


FIG.  191. 


FIG.  192. 


this  connection,  it  is  necessary  that  each  transformer  be  provided 
with  two  secondary  windings.  Thus,  the  windings  a  and  a! 
are  on  the  same  core.  Likewise,  b  and  bf  and  c  and  cf  are  on  the 
same  cores.  The  windings  are  connected  as  shown.  The  coils 

a  and  a',  b  and  bf  and  c  and  c'  are 
so  connected  that  their  e.m.fs. 
oppose  one  another.  This  might 
not  be  apparent  from  the  dia- 


FIG.  193. 


FIG.  194. 


gram.     To  avoid  crossings  of  the  lines  the  connections  here  are  as 
though  they  were  helping  one  another. 

Figure  191  shows  a  connection  known  as  the  double  Y  connec- 
tion.    This  is  the  same  as  Fig.  189  provided  the  neutral  points 


25(5      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

in  the  latter  are  connected.  Figure  192  is  a  double  delta  con- 
nection. As  before,  the  coils  a  and  a',  b  and  b'  and  c  and  c'  are  on 
the  same  cores. 

Two-phase  or  four-ring  rotaries  are  not  in  common  use.  In 
Fig.  193,  however,  is,  shown  the  diametral  connection  of  a  four- 
ring  rotary,  and  Fig.  194  is  a  corresponding  delta  connection. 

In  these  descriptions,  it  has  been  assumed  that  three  trans- 
formers are  used  in  the  case  of  three  phase,  or  two  transformers 
for  two  phase.  It  will,  however,  be  apparent  that  instead  of  the 
two  or  three  transformers,  one  polyphase  transformer  might 
have  been  employed.  This  is  often  done,  since  as  explained  in 
the  chapter  on  transformers,  a  polyphase  transformer  costs  less 
than  the  corresponding  number  of  single-phase  transformers. 

238.  Rotary  Converters  Versus  Motor-generator  Sets.— 
Besides  the  method  of  converting  from  an  alternating  to  a  con- 
tinuous current  by  means  of  a  rotary  converter  as  described  in 
the  preceding  pages,  it  is  also  possible  to  accomplish  the  same 
result  by  means  of  a  motor-generator  set.  The  two  machines 
are  commonly  mounted  on  the  same  shaft,  and  the  set  is  fre- 
quently provided  with  only  two  bearings. 

The  alternating-current  motor  of  such  a  set  may  be  either  an 
induction  motor  or  a  synchronous  motor.  The  latter  is  the  one 
usually  employed.  The  two  most  troublesome  points  in  connec- 
tion with  a  synchronous  motor  are  the  matter  of  starting  and  the 
provision  of  direct  current  for  the  fields.  With  a  set  changing 
from  alternating  to  direct  current,  both  of  these  objections  usu- 
ally disappear.  Direct  current  is  almost  always  available,  since 
most  direct-current  systems  include  a  storage  battery  on  the 
line,  or  if  not,  only  one  machine  need  be  started  from  the  alter- 
nating-current end,  and  the  rest  started  from  the  continuous 
current  of  the  first  machine.  In  any  event,  the  machine  is 
started  without  load  and  starting  is  therefore  a  comparatively 
easy  matter.  Direct  current  for  the  field  excitation  of  the 
synchronous  motor  is,  of  course,  available  as  soon  as  the  set  is  in 
motion  and  ready  for  it.  The  synchronous  machine  is  slightly 
more  efficient  than  the  induction  machine,  and  the  ability  to 
regulate  the  power  factor  is  of  great  advantage.  It  is,  however, 
common  practice  when  there  are  several  motor-generator  sets  in 
the  same  substation  to  provide  one  of  them  with  an  induction 
motor,  and  the  remainder  with  synchronous  motors.  This  in- 
sures one  set  which  can  be  readily  started  at  any  time. 


THE  ROTARY  CONVERTER  257 

239.  Cost. — In  comparing  the  advantages  of  the  rotary  con- 
verter and  the  motor-generator,  the  first  consideration  is  the 
relative  costs  of  the  two  forms  of  apparatus.     However,  it  is 
necessary  to  consider  not  only  the  rotary  on  the  one  hand  and  the 
motor-generator  set  on  the  other,  but  also  the  auxiliary  apparatus. 
The  first  point  is  that  the  rotary  almost  invariably  calls  for  the 
use  of  transformers  to  reduce  the  line  e.m.f.  to  that  required  by 
the  rotary.     The  synchronous  motor  of  the  motor-generator  set,  on 
the  other  hand,  can  in  many  cases  be  wound  to  operate  at  the  line 
potential.     The  rotary,  in  addition  to  the  transformers,  requires 
in  general  some  method  of  regulating  the  direct  voltage.     This, 
as  previously  explained,  may  take  the  form  of  reactors  connected 
in  the  line,  of  an  induction  regulator,   a  special  synchronous 
machine  mounted  on  the  rotary  shaft  or  of  a  split-pole  rotary. 
No  matter  what  the  method  adopted,  there  will  be  some  extra 
cost  on  account  of  the  regulating  arrangements.     On  the  other 
hand,  the  motor-generator  set  consists  of  two  machines,  and 
each  of  these  must  be  somewhat  larger  than  the  rotary  which 
would  replace*  both  of  them.     Considering  everything,  the  cost 
of  the  motor-generator  set  will  be  appreciably  higher  than  that 
of  the  rotary. 

240.  Frequency. — As  already  pointed  out,   rotaries  are  not 
very  well  adapted  to  operation  on  60-cycle  circuits.     The  motor- 
generator  set  is  entirely  relieved  of  this  difficulty  as  far  as  the 
direct-current  generator  is  concerned,  as  the  generator  may  have 
any  convenient  number  of  poles,  irrespective  of  the  number  of 
poles  of  the  synchronous  machine.     It  is,  moreover,  practicable 
to  design  synchronous  motors  for  either  60  or  25  cycles.     For  60- 
cycle  installations  then,  the  motor-generator  set  is  frequently  to 
be  preferred. 

241.  Efficiency. — In  the  matter  of  efficiency,  the  rotary  has  a 
distinct  advantage  as  it  has  the  losses  of  only  one  machine  in- 
stead of  two.     The  losses  in  the  transformers  and  in  the  regulat- 
ing apparatus  will  offset  this  advantage  to  a  certain  extent,  but 
the  efficiency  of  the  rotary  and  the  necessary   auxiliary  appa- 
ratus will  average  from  2  to  3  per  cent,  higher  than  that  of  the 
motor-generator  set. 

242.  Regulation. — The  matter  of  the  voltage  regulation  in  the 
two  methods  of  transformation  is  of  importance.     There  are  two 
classes  of  variations  to  which  the  incoming  power  on  the  alternat- 
ing-current line  is  subject,  namely,  variations  in  voltage  and  varia- 

17 


258      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

tions  in  frequency.  The  latter  is  the  easier  to  take  care  of,  since 
in  the  case  of  large  stations,  particularly  if  provided  with  turbine- 
driven  units,  the  frequency  is  remarkably  constant.  This  is,  of 
course,  to  be  expected,  since  on  account  of  all  of  the  machines 
operating  in  synchronism,  small  variations  of  the  individual 
governors  will  have  but  little  effect  upon  the  frequency  of  the 
current  generated  by  the  station.  It  is  not  so  easy  to  prevent 
fluctuations  of  the  voltage  at  the  receiving  end,  particularly  when 
the  power  is  supplied  to  a  number  of  substations,  each  with  a 
varying  load. 

The  motor-generator  set  is  not  affected  at  all  by  variations  of 
voltage  unless  the  fluctuations  are  so  violent  that  the  machines 
will  not  remain  in  step.  As  long  as  the  alternating  voltage  re- 
mains anywhere  near  constant,  the  synchronous  motor  will 
continue  to  operate  at  the  same  speed,  and  consequently  the 
voltage  of  the  continuous-current  machine  will  not  be  affected 
by  the  variations  in  the  voltage  of  the  supply. 

•In  the  case  of  the  rotary,  on  the  other  hand,  the  voltage  at 
the  continuous-current  end  bears  a  nearly  constant  relation  to 
that  of  the  alternating-current  end.  Any  variation,  therefore, 
in  the  voltage  of  the  supply  is  immediately  reproduced  in  the 
same  proportion  at  the  direct-current  end.  In  this  respect,  the 
rotary  is  distinctly  inferior  to  the  motor-generator  set. 

If  variations  of  frequency  are  considered,  the  case  would  be 
exactly  reversed.  The  rotary  would  not  be  affected  at  all, 
while  all  fluctuations  would  be  reproduced  at  the  direct-current 
commutator  in  the  case  of  the  motor-generator  set.  However, 
variations  of  frequency  are  not  of  importance,  to  nearly  the  same 
extent  as  are  those  of  voltage. 

243.  The  Cascade  Converter. — It  will  be  shown  in  the  chapter 
upon  the  induction  motor,  that  it  is  possible  to  operate  two 
induction  motors  in  cascade  or  concatenation.  One  of  the  two 
motors  is  connected  to  the  line  in  the  usual  manner.  This  motor 
must  be  provided  with  a  wound  rotor.  The  current  for  the 
primary  of  the  second  motor  is  supplied  by  the  secondary  of  the 
first.  The  secondary  or  rotor  of  the  second  motor  may  be 
either  of  the  wound-rotor  type  or  of  the  squirrel-cage  type. 
If  the  two  machines  have  the  same  number  of  poles,  the  set  will 
rotate  at  slightly  less  than  half  the  synchronous  speed  of  either 
machine.  In  any  event,  the  speed  will  be  that  corresponding 


THE  ROTARY  CONVERTER  259 

to  a  machine  having  as  many  poles  as  the  sum  of  the  poles  on 
the  two  machines. 

There  is  no  reason  why  we  may  not  substitute  a  synchronous 
motor  for  the  second  induction  motor.  In  this  case,  the  set  will 
rotate  at  the  synchronous  speed  corresponding  to  a  machine  of  the 
total  number  of  poles.  If  the  field  of  the  synchronous  machine 
is  so  adjusted  that  this  machine  operates  at  unity  power  factor, 
the  power  factor  of  the  combined  set  will  be  somewhat  less  than 
unity,  as  lagging  current  will  be  required  to  produce  the  flux  of 
the  first  machine.  If  the  field  of  the  synchronous  machine  is 
made  stronger,  the  combined  set  may  be  caused  to  have  a  power 
factor  of  unity,  or  to  take  a  leading  current. 

If  in  place  of  the  synchronous  motor  a  rotary  converter  is 
substituted,  the  operation  will  be  essentially  the  same.  In- 
stead of  taking  mechanical  power  out  of  the  machine,  current 
may  be  taken  from  the  commutator  of  the  rotary.  If  the  two 
machines  have  the  same  number  of  poles,  the  speed  will  be  half 
the  synchronous  speed  of  either.  The  frequency  of  the  current 
supplied  to  the  rotary  will  be  half  the  line  frequency.  Thus  if 
the  line  frequency  is  60  cycles,  the  frequency  of  the  current 
applied  to  the  rotary  will  be  30  cycles.  Hence,  a  machine  of 
this  character  removes  most  of  the  difficulties  connected  with 
60-cycle  converters. 

In  a  cascade  converter,  if  the  two  machines  have  the  same 
number  of  poles,  half  of  the  power  received  by  the  induction 
motor  is  transformed  to  mechanical  power  and  appears  at  the 
shaft.  The  other  half  is  transformed  to  electrical  power  at 
half  of  the  line  frequency.  The  rotary  converter,  therefore,  re- 
ceives half  of  its  power  as  mechanical  power  through  the  shaft, 
and  the  other  half  as  electrical  power.  It  therefore  combines 
the  functions  of  a  rotary  converter  and  those  of  a  continuous- 
current  generator. 

It  has  been  shown  that  both  the  induction  motor  and  rotary 
converter  are  improved  by  increasing  the  number  of  phases. 
There  are  obvious  objections  to  employing  a  great  number  of 
phases  in  primary  circuits.  The  circuit  between  the  secondary 
of  the  induction  motor  and  the  rotary,  however,  is  never  opened, 
and  these  objections  lose  their  weight.  It  is  therefore  customary 
to  wind  the  secondary  of  the  motor  for  from  six  to  twelve  phases. 
There  is  no  need  of  slip  rings  on  either  the  induction  motor  or 
on  the  rotary,  since  by  using  only  two  bearings  for  the  set, 


260      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


it  is  possible  to  take  the  current  directly  from  one  to  the  other. 
The  cross  connections  may  therefore  be  made  numerous  without 
complication. 

Such  a  set  may  be  started  by  applying  current  to  the  primary 
of  the  induction  motor  in  the  usual  way.  The  starting  torque 
will,  however,  be  small,  since  the  losses  in  both  rotors  will  be 
small,  but  it  may  be  increased  if  necessary  by  opening  up  the 
secondary  winding  of  the  induction  motor  at  the  opposite  ends 
from  these  connected  to  the  rotary  windings,-  and  inserting 


FIG.  195. 

resistance  for  starting.  If  direct  current  is  available,  the  set 
can  be  started  from  the  direct-current  end. 

The  principal  advantage  of  such  a  set  over  a  rotary  converter 
is  that  it  is  well  adapted  to  operation  on  50  or  60  cycles.  It 
is  also  easy  to  control  the  voltage  if  only  a  moderate  variation 
is  desired,  since  the  primary  and  secondary  of  the  induction 
motor  will  usually  have  sufficient  reactance  to  allow  con- 
siderable voltage  regulation  by  changing  the  field  current  of  the 
rotary. 

244.  The  Mercury  Arc  Rectifier. — Practically  all  transforma- 
tion of  alternating  to  direct  current  on  a  large  scale  is  accom- 


THE  ROTARY  CONVERTER 


261 


H 


I yVWWWWW ' 

Transformer 

— wwvwv — IG 


A.C.Supply 


i® 


© 


plished  by  means  of  the  rotary  converter  or  the  motor-generator 
set.  For  certain  classes  of  work  where  only  a  small  amount  of 
power  is  to  be  transformed,  the  low  first  cost  and  the  simplicity 
of  operation  of  certain  other  devices  may  make  them  pref- 
erable. The  mercury  arc  rectifier  falls  within  this  class. 

The  general  appearance  of  a  mercury  arc  rectifier  is  shown  in 
Fig.  195.  The  principal  element  is  a  vessel,  usually  of  glass, 
from  which  the  air  has  been  exhausted.  The  vessel  has  one 
electrode  formed  by  a  pool  of  mercury  and  two  other  electrodes 
of  iron  or  graphite.  With  no  current  passing,  the  resistance 
between  any  two  electrodes  is  very 
high.  If,  however,  an  arc  is  once 
started  the  resistance  for  a  current  pass- 
ing from  the  iron  or  graphite  electrode 
to  the  mercury  is  low;  but  the  resis- 
tance to  current  passing  in  the  oppo- 
site direction  is  very  high.  In  fact, 
practically  no  current  can  pass  even 
at  a  pressure  of  several  thousand  volts. 

The  connections  are  shown  in  Fig. 
196.  The  coils  E  and  F  are  con- 
structed so  as  to  have  high  reactance 
and  low  resistance.  A  slight  tilting 
of  the  tube  causes  the  mercury  to 
bridge  over  from  B  to  C  and  current 
flows  through  this  bridge  and  the 
resistor  connected  to  C.  When  the 

connection  through  the  mercury  bridge  breaks,  a  flash  is  pro- 
duced inside  the  tube  and  current  can  at  once  flow  through 
the  main  circuit.  The  auxiliary  circuit  through  C  and  the 
resistor  is  then  opened. 

If  at  any  given  instant  the  terminal  A  is  positive,  current 
will  flow  from  it  through  the  tube  and  out  at  the  terminal  B. 
It  then  passes  through  the  battery  J,  or  other  load,  the  reactor 
E  and  back  to  the  transformer.  An  instant  later  the  trans- 
former has  reversed  its  polarity,  the  terminal  A'  becomes  positive 
and  the  current  passes  from  A'  to  B,  the  terminal  A  remaining 
inactive.  Thus  the  direction  of  the  current  is  always  the  same 
through  the  battery  J.  The  function  of  the  reactors  is  to  pre- 
vent sudden  changes  of  the  current.  Thus  the  times  when  the 
current  would  be  zero  may  be  bridged  over  and  a  nearer  approach 


0 


-=•  j 


TI® 

^TKKKr^fflKK5^ 
©  ~z 

F  E 

FIG.  196. 


262      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

to  a  steady  continuous  current  produced.  This  also  lessens 
the  liability  of  the  arc  to  go  out  while  the  current  is  passing 
through  zero,  thus  stopping  the  action.  Figure  197  shows  an 
oscillogram  of  the  applied  alternating  voltage  and  the  resultant 
direct  current.  It  will  be  seen  that  the  latter  is  by  no  means 
steady,  although  it  is  .all  in  the  same  direction. 

The  fact  that  the  current  delivered  is  not  steady  is  a  dis- 
advantage if  an  attempt  is  made  to  use  it  to  drive  a  continuous- 
current  motor.  Such  a  motor  can  be  operated  but  with 
considerably  increased  losses  due  to  hysteresis  and  eddy  currents. 
A  more  serious  objection  is  the  fact  that  if  the  current  drops 
below  a  certain  percentage  of  its  full-load  value,  the  arc  will  go 


Direct  Current 


Alternating  Voltage 

FIG.  197. 

out  and  the  action  cease.  If  the  load  on  a  motor  becomes  very 
light  it  is  therefore  likely  to  stop. 

Neither  of  these  objections  apply  to  the  charging  of  small 
storage  batteries  and  mercury  arc  rectifiers  are  extensively  used 
for  this  purpose  in  places  where  continuous  current  is  not  avail- 
able. The  rectifying  outfit  is  reasonable  in  first  cost,  requires 
little  attention,  and  gives  good  efficiency. 

At  the  present  time,  serious  efforts  are  being  made  to  de- 
velop the  mercury  arc  rectifier  in  larger  sizes,  with  particular 
reference  to  its  use  on  electric  locomotives.  It  would  then  be 
possible  to  transmit  power  to  the  locomotive  by  means  of  single- 
phase  currents.  The  voltage  would  be  stepped  down  by  means 
of  transformers  on  the  locomotive,  and  the  current  changed  to 
direct  current  by  the  rectifier. 


THE  ROTARY  CONVERTER  263 


PROBLEMS 

97.  An  eight-pole  rotary  converter  has  480  conductors  on  the  armature 
connected  to  a  240-bar  commutator.     The  winding  is  a  simplex  lap.     One 
of  the  rings  is  connected  to  commutator  bar  No.  1.     To  what  other  commu- 
tator bars  must  this  same  ring  be  connected? 

98.  If  the  machine  is  a  two-ring  rotary,  to  what  commutator  bars  must 
the  other  ring  be  connected? 

99.  In  the  case  of  a  four-ring  rotary,  state  the  connections  of  the  rings  to 
the  commutator  bars. 

100.  What  will  be  the  connections  for  a  three-ring  rotary? 

101.  A  four-ring  rotary  generates  a  d.-c.  voltage  of  250.     The  a.-c.  supply 
voltage    is  at  44,000  volts.     What  is  the  ratio  of  the  turns  on  the  trans- 
formers, making  no  allowance  for  the  drop  in  the  rotary?     What  is  the 
correct  ratio  for  a  three-ring  rotary? 

102.  A  three-ring  rotary  has  a  d.-c.  voltage  of  600.     The  supply  voltage 
is  22,000.     Allowing  a  drop  of  5   per  cent,   in  the  rotary  windings,  and 
assuming  that  the  transformers  are    connected  in  delta    on   the   primary 
side  and  in  star  on  the  secondary,  what  is  the  ratio  of  the  primary  to  the 
secondary  turns? 


CHAPTER.  XVIII 
THE  INDUCTION  MOTOR 

245.  General  Description. — A  view  of  a  complete  induction 
motor  is  shown  in  Fig.  198  and  an  "exploded  view"  giving  an 
idea  of  the  construction  of  the  various  parts  is  shown  in  Fig.  199. 
The  stationary  part  is  ordinarily  known  as  the  stator  while  the 
rotating  member  is  called  the  rotor.  An  idea  of  the  relative 
dimensions  and  arrangement  of  the  stator  laminations  and  slots 
may  be  gained  from  Fig.  200.  The  air  gap  of  an  induction  motor 


FIG.  198. 

is  always  as  short  as  it  is  safe  to  make  it  and  in  consequence  the 
shaft  and  bearings  are  heavy. 

246.  The  Stator. — The  stator,  both  in  its  mechanical  construc- 
tion and  in  its  winding  is  the  same  as  the  armature  or  stator  of  a 
synchronous  machine.     In  fact,  it  is  always  possible  to  remove 
the  rotor  from  an  induction  motor  and  by  substituting  for  it  a 
revolving  field,  to  convert  the  machine  into  an  alternator  or 
synchronous  motor. 

247.  The  Rotor.— The  rotor  shown  in  Fig.  199  is  of  the  type 
known  as  a  squirrel-cage  rotor.     The  "winding"   consists  of 

264 


THE  INDUCTION  MOTOR 


265 


bars  of  copper  passed  through  the  rotor  slots  and  all  connected 
together  at  the  ends  by  rings  of  copper  or  brass.  These  latter  are 
known  as  end  rings.  The  insulation  on  the  rotor  bars  is  light 
and  in  many  cases  is  omitted  altogether. 


FIG.  199. 

Another  form  of  rotor  known  as  a  wound  rotor  is  shown  in 
Fig.  201.  The  winding  on  this  is  identical  with  that  of  a  rotating 
armature  alternator  and  is  therefore  the  same  in  principle  as  that 
of  the  stator.  The  ends  are 
brought  to  three  slip  rings. 
This  winding  is  always  three 
phase  although  the  stator  may 
be  wound  for  one,  two  or  three 
phases.  It  is  essential  that  the 
rotor  winding  be  polyphase, 
and  since  the  three  phase  is 
simpler  than  the  two  phase 
and  at  the  same  time  is  better, 
it  is  always  used.  A  slight  ad- 
vantage could  be  gained  by 
winding  for  a  greater  number 

of  phases,  but  the  gain  is  not  great  enough  to  offset  the  complica- 
tion incident  to  using  more  than  three  rings. 


Stator  48  Slots 
Slot  Pitch 
1.113 


Botor  110  Slots 

Slot  Fitch 

0.487 


0.035" 


FIG.  200. 


266     PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

248.  The  Rotating  Magnet  Field. — On  applying  current  to  a 
polyphase  stator,  a  rotating  magnetic  field  is  set  up.  This 
subject  has  been  fully  treated  in  Chaps.  14  and  16  in  connection 
with  the  operation  of  synchronous  machines.  It  is  unnecessary 


FIG.  201. 

to  repeat  the  discussion  here.     The  facts,  however,  should  be 
carefully  reviewed  before  proceeding  further. 

249.  The  Production  of  Current  in  the  Rotor. — Figure  202 
shows  a  portion  of  the  surface  of  a  rotor.  The  shaded  parts  are 
supposed  to  represent  the  " poles"  of  the  stator  magnetism  as 
they  pass  over  the  rotor  winding.  It  is  understood  that  the 


FIG.  202. 

magnetism  is  not  confined  to  definite  rectangles  as  shown,  but 
varies  from  a  maximum  at  the  middle  of  the  rectangles  to  zero 
midway  between  them.  A  field  magnet  rotating  outside  the 
rotor  would  give  essentially  the  same  results. 

Suppose  the  rotor  to  be  at  rest.     As  the  poles  pass  over  the 
surface  they  will  induce  e.m.fs.  in  the  rotor  bars.     These  e.m.fs. 


THE  INDUCTION  MOTOR  267 

will  be  greatest  at  the  points  where  the  flux  is  greatest  and  will,  in 
fact,  be  proportional  to  the  flux  at  any  point.  The  e.m.fs. 
in  the  various  bars  are  indicated  in  Fig.  202  by  means  of  arrows. 
These  are  drawn  longest  directly  under  the  center  of  the  poles  and 
gradually  shorter  as  the  bars  midway  between  the  poles  are 
approached.  The  frequency  of  the  e.m.fs.  in  the  rotor  when  the 
latter  is  at  rest,  will  be  the  same  as  the  line  frequency. 

250.  Rotor  Current. — If  the  rotor  were  non-inductive  the  same 
arrows  used  in  Fig.  202  to  indicate  the  e.m.fs.  of  the  various 
bars  might  also  be  considered  as  indicating  the  currents.     This 
however  is  not  the  case.     The  current  as  it  passes  through  the 
bars  and  through  the  end  rings,  sets  up  leakage  fluxes.     These 
fluxes  set  up  an  additional  e.m.f.  in  the  rotor  bars  and  therefore 
cause  the  current  to  lag  behind  the  e.m.f.     As  a  consequence  the 
sheets  of  current  will  be  displaced  some  distance  to  one  side  or  the 
other  of  the  sheets  of  e.m.f.     If  the  flux  be  considered  as  moving 
from  left  to  right,  the  sheets  of  current  will  lie  to  the  left  of  the 
sheets  of  e.m.f. 

251.  Production  of  Torque. — Whenever  a  current  lies  across  a 
magnetic  field  a  force  is  produced  tending  to  force  the  current 
out  of  the  field  or  to  force  the  field  away  from  the  current.     The 
induction  motor  has  this  condition  and  consequently  the  motor 
tends  to   start.     This  starting  torque  would  be  a  maximum  if 
the  sheets  of  current  coincided  with  the  sheets  of  flux  and  conse- 
quently of  e.m.f.     Unfortunately,  as  just  explained,  this  is  not 
the  case.     The  sheets  of  current  are  displaced  to  one  side  so  that 
the  maximum  of  the  current  sheet  does  not  coincide  with  the 
maximum  of  the  flux  sheet.     As  the  current  sheets  are  displaced 
it  will  be  evident  that  in  any  given  flux  sheet  some  conductors 
will  be  carrying  current  toward  the  observer  and  other  con- 
ductors carrying  current  from  him.     The  forces  on  these  two 
sets  of  conductors  will  be  in  opposite  directions  and  consequently 
the  torque  will  be  reduced.     If  the  lag  of  the  current  were  90°, 
the  net  torque  would  be  zero.     An  exactly  similar  condition  was 
found  in  connection  with  the  study  of  the  synchronous  machine, 
and  it  would  be  well  to  refer  again  to  Figs.  159,  163,  and  164  and 
the  accompanying  descriptions. 

In  the  induction  motor  with  squirrel-cage  rotor  the  reactance 
of  the  rotor  is  usually  greater  than  the  resistance.  The  lag  at 
starting  is  therefore  great,  usually  about  60°  and  the  starting 
torque  for  a  given  current  and  flux  is  consequently  small.  To 


268      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

start  a  load  requiring  a  torque  equal  to  the  full-load  torque  of  the 
motor  requires  about  five  times  full-load  current. 

252.  Influence  of  the  Resistance  of  the  Rotor  upon  Starting 
Torque. — If  the  resistance  of  the  rotor  of  an  induction  motor 
were  zero,  the  lag  of  the  current  behind  the  e.m.f.  would  be  90° 
and  the  starting  torque  would  be  zero.     The  greater  the  resistance 
of  the  rotor,  the  greater  the  starting  torque  for  a  given  current,  but 
the  less  the  current.     There  is  a  " happy  mean"  and  it  is  reached 
when  the  resistance  is  equal  to  the  reactance  or  the  lag  of  the  cur- 
rent is  45°.     It  would  not  be  desirable  to  have  the  resistance  of 
the  rotor  of  an  ordinary  squirrel-cage  induction  motor  so  great  as 
this  as  the  efficiency  of  the  motor  would  be  very  low.     It  is, 
however,  necessary  in  most  cases  to  make  the  resistance  far 
greater  than  it  need  be,  that  is,  ordinarily  the  current  density  in 
the  end  rings  is  made  far  higher  than  that  in  the  bars,  and  more- 
over the  end  rings  are  made  of  high  resistance  material  such  as 
cast  copper  or  brass.     This  added  resistance  is  a  detriment  after 
the  motor  is  up  to  full  speed.     It  is  a  necessary  evil,  used  only  to 
improve  the  starting  torque. 

253.  The  Use  of  the  Wound  Rotor. — By  using  an  induction 
motor  with  a  wound  rotor  it  becomes  possible  to  adjust   the 
resistance  of  the  rotor  circuit  to  the  proper  value  to  suit  the 
conditions.     Thus  the  resistance  may  be  made  such  as  to  give 
the  maximum  starting  torque  (or  may  be  made  even  greater  so  as 
to  take  as  small  a  current  as  possible  and  still  start  the  load) 
and  this  resistance  may  be  cut  out  as  the  motor  attains  speed  so 
that  the  machine  is  at  all  times  operating  under  the  best  possible 
conditions.      A    wound-rotor   induction    motor    costs    approxi- 
mately 35  per  cent,  more  than  a  corresponding  squirrel-cage 
machine,  but  the  added  cost  is  frequently  justified  in  the  case  of 
motors  which  have  to  start  frequently  under  heavy  loads,  or  in 
the  case  of  those  whose  speed  must  be  adjustable. 

254.  Conditions  at   Normal   Speed. — As   just   shown,    when 
current  is  applied  to  the  stator  of  a  polyphase  induction  motor 
the  rotor  develops  torque  and  the  motor  will  start  from  rest. 
As  the  motor  speeds  up,  since  the  rotor  is  moving  in  the  same 
direction  as  the  rotating  magnetic  field  the  rate  of  cutting  of  the 
magnetic   lines   becomes   less.     Consequently   both   the   e.m.f. 
induced  in  the  rotor  bars  and  the  frequency  of  the  e.m.f.  and 
current  become  less  and  finally  reach  zero  at  synchronism,  that  is, 


THE  INDUCTION  MOTOR  269 

when  the  rotor  surface  and  the  flux  are  moving  at  the  same  speed. 
Synchronous  speed  is  then  the  limiting  speed  of  the  motor.  Its 
speed  will  always  fall  short  of  synchronous  speed  by  an  amount 
such  that  sufficient  current  will  be  induced  in  the  rotor  to  develop  the 
torque  necessary  to  keep  the  motor  in  rotation.  If  the  external  load 
is  zero,  only  enough  torque  will  be  required  to  overcome  the 
friction  and  the  speed  will  drop  below  synchronism  by  only  a 
fraction  of  1  per  cent.  As  the  load  is  increased,  the  speed  de- 
creases and  this  can  continue  until  the  load  becomes  so  great 
that  the  motor  is  unable  to  carry  it  and  it  will  "pull  out"  and 
stop.  When  the  motor  is  in  operation  it  is  said  to  have  a  certain 
amount  of  slip.  Slip  is  the  difference  between  the  synchronous 
speed  and  the  actual  speed  divided  by  the  synchronous  speed. 
Thus,  if  the  synchronous  speed  were  1200  r.p.m.  and  the  motor 
were  operating  at  1100  r.p.m.  the  slip  would  be  8.33  per 
cent.  The  slip  at  full  load  may  be  as  low  as  1  per  cent,  in  the 
case  of  large  motors  or  as  great  as  15  per  cent,  for  very  small 
ones. 

Imagine  a  motor  operating  at  full  load  with  a  slip  of  say 
5  per  cent.  If  the  line  frequency  is  60  cycles  per  second,  the 
frequency  of  the  current  in  the  rotor  will  be  only  5  per  cent,  of 
this  or  3  cycles  per  second.  The  resistance  and  the  inductance 
of  the  rotor  are  the  same  as  at  standstill  but  the  reactance  (which 
is  equal  to  2ir  times  the  inductance  times  the  frequency)  will 
be  only  5  per  cent,  as  great  as  at  standstill.  Consequently,  the 
lag  of  the  rotor  current  behind  the  e.m.f.  will  be  small  and  the 
torque  per  ampere  in  the  rotor  will  be  much  larger  than  at 
standstill.  In  other  words,  the  power  factor  of  the  rotor  at 
load  will  be  far  higher  than  at  standstill. 

255.  Speeds  of  Induction  Motors. — As  has  been  pointed  out, 
the  rotor  of  an  induction  motor  tends  to  revolve  at  the  same 
speed  as  the  rotating  magnetic  field.  In  practice  the  actual 
speed  under  full  load  will  be  from  1  to  5  per  cent,  less  than  this. 
This  fact  limits  the  possible  speeds  of  induction  motors.  Thus 
in  a  60-cycle,  two-pole  motor  the  flux  revolves  sixty  times  a 
second  or  3600  r.p.m.  No  higher  speed  than  this  is  possible 
(with  60  cycles  current)  since  we  can  not  have  less  than  two 
poles.  The  next  possible  number  of  poles  is  four  giving  a 
speed  of  1800  r.p.m.  The  following  table  gives  the  common 
speeds: 


V' 

~v    \/ 


270      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 


Number  of  poles 

R.p.m.  60  v. 

R.p.m.  25  v. 

2 

3600 

1500 

4 

1800 

750 

6 

1200 

500 

8 

900 

375 

10 

720 

300 

12 

600 

250 

Two-pole  motors  are  rarely  used,  since  they  are  difficult  to 
wind.  The  above  speeds  apply  also  to  synchronous  machines. 

256.  The  Induction  Generator. — As  we  have  just  shown,  it 
is  impossible  for  the  induction  motor  to  operate  as  a  motor  at  a 
speed  above  synchronism.  If,  however,  we  apply  power  to  the 
shaft  by  means  of  a  steam  engine  or  otherwise,  it  may  be  forced 
to  rotate  faster.  The  rotor  bars  will  again  be  cutting  the  flux 
but  in  the  opposite  direction  from  that  in  the  machine  operating 
as  a  motor.  The  direction  of  the  e.m.f.  at  any  instant  will 
therefore  be  reversed,  the  current  will  flow  in  the  opposite  direc- 
tion and  the  torque  will  be  reversed.  As  a  consequence,  instead 
of  the  torque  being  in  the  direction  of  the  rotation  as  in  a  motor, 
it  will  be  opposed  to  it,  or  the  machine  will  operate  as  a  generator. 

The  machine  differs,  however,  from  the  ordinary  generator  in 
several  respects.  It  will  not  generate  alone,  that  is,  it  will 
operate  only  on  a  line  already  connected  to  a  synchronous 
machine.  Both  the  frequency  and  the  voltage  of  the  line  will 
be  determined  by  the  synchronous  machine.  All  regulation  of 
the  voltage  must  therefore  be  accomplished  by  means  of  the 
field  rheostat  of  the  synchronous  machine. 

On  acount  of  these  facts  the  field  of  application  of  the  induc- 
tion generator  is  rather  limited.  Some  electric  locomotives 
are  operated  by  means  of  induction  motors.  When  the  train  is 
descending  a  grade  at  a  speed  slightly  above  that  corresponding 
to  the  synchronous  speed  of  the  motors,  the  latter  automatically 
become  generators,  and  return  power  to  the  line. 

Induction  generators  are  occasionally  used  in  the  development 
of  small  water  powers.  Thus  a  small  fall  may  be  available  on  or 
near  one  of  the  lines  of  a  power-distributing  system.  The  avail- 
able power  may  be  so  small  that  it  is  not  practicable  to  install  a 
power  house  with  attendants  to  regulate  the  voltage,  etc.,  but  it 
may  be  worth  while  to  install  a  simple  water-wheel,  probably 
without  a  governor,  and  an  induction  generator.  An  overspeed 
device  would  be  desirable  to  disconnect  the  induction  generator 


THE  INDUCTION  MOTOR  271 

from  the  line  and  stop  the  water-wheel  in  case  the  power  supply 
to  the  line  should  fail.  The  generator  would  be  run  up  to  speed, 
connected  to  the  line  and  the  gate  of  the  waterwheel  opened. 
The  installation  would  then  be  left  alone  except  for  a  daily  in- 
spection. The  frequency  and  voltage  would  be  controlled  from 
the  other  stations  operating  on  the  line.  The  induction  gener- 
ator would  continue  to  supply  to  the  line  an  amount  of  power 
corresponding  to  the  power  developed  by  the  fall. 

Another  use  is  in  connection  with  the  generation  of  continuous 
current  by  means  of  turbine-driven  generators.  The  con- 
tinuous-current, turbine-driven  generator  in  large  sizes  presents 
great  difficulties  in  design.  They  are  consequently  manufactured 
only  in  comparatively  small  sizes.  A  synchronous  generator 
may  be  built  and  its  output  rectified  by  means  of  a  rotary 
converter.  A  somewhat  simpler  outfit  consists  of  an  induction 
generator  and  a  synchronous  converter.  The  operation  is  par- 
ticularly convenient  since  there  is  no  field  on  the  generator  to 
be  adjusted.  The  induction  machine  will  not  excite  itself,  and 
it  is  necessary  that  the  rotary  converter  be  driven  at  a  moderate 
rate  of  speed  by  some  outside  source  of  power  before  it  is  con- 
nected to  the  induction  machine.  There  is  of  course  no  necessity 
for  synchronizing  the  two  machines  nor  is  it  even  necessary  that 
the  speeds  be  very  nearly  correct  before  they  are  connected 
together. 

257.  Vector  Diagrams  of  the  Induction  Motor. — Consider  a 
wound-rotor  induction  motor  in  which  there  are  the  same 
number  of  turns  on  the  stator  and  on  the  rotor.  If  there  is 
no  connection  between  the  slip  rings,  that  is,  no  resistors  con- 
nected across  them,  and  current  is  applied  to  the  stator  the  ma- 
chine will  not  revolve.  If  the  voltage  across  the  slip  rings  be 
tested,  we  shall  find  that  there  is  present  a  three-phase  voltage 
equal  to  the  primary  voltage.  The  frequency  will  be  the 
same  as  the  frequency  of  the  current  applied  to  the  stator. 
If  the  rotor  is  held  so  that  it  can  not  revolve,  current  could  be 
taken  from  the  slip  rings  and  used  to  supply  a  load.  The  ma- 
chine would  then  be  acting  as  a  transformer.  Transformers  are 
not  built  in  this  manner  as  the  usual  construction  is  cheaper  and 
better. 

If  the  motor  is  allowed  to  rotate  at  half  speed,  the  rotor 
bars  will  be  moving  half  as  fast  as  the  rotating  flux,  and  half 
voltage  and  half  frequency  will  be  obtained  at  the  slip  rings. 


272      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

Half  the  power  supplied  to  the  primary  (neglecting  losses)  will 
appear  as  electric  power  in  the  secondary  circuit,  the  other  half 
will  appear  as  mechanical  power  at  the  shaft. 

The  induction  motor  may  be  regarded  as  a  general  type  of 
transformer,  capable  of  transforming  electric  power  either  to 
mechanical  power  or  to  electirc  power  or  to  both  at  the  same 
time.  The  ordinary  transformer  then  is  a  special  form  of  trans- 
former, not  capable  of  receiving  or  of  giving  out  mechanical 
power. 

These    considerations   lead   one   to   expect   that   the   vector 

diagrams  of  the  induction  motor  will  be  very  similar  to  those 

of  the  transformer,  and  in  fact  this  is  the  case. 

Es  Thus,  Fig.  203  shows  the  conditions  at  no  load. 

The  flux  is  indicated  by  the  vector  marked  $. 

The  direction  of  the  e.m.f.  induced  in  both  the 

stator  and  in  the  rotor  is  indicated  by  the  vector 

in  marked   Er.     At  no  load  the   motor  operates 

^—- *-$  practically   in    synchronism.      The    rotor    bars 

therefore  do  not  cut  the  flux  and  the  rotor  e.m.f. 
is   practically   zero.     The  rotor  current  is  also 
practically  zero   and   may  be   neglected.     The 
current  in  the  stator  winding  produces  the  flux 
and  is  therefore  nearly  in  phase  with  it.     It, 
FIG.  203.         however,  leads  the  flux  by  a  slight  angle  on  ac- 
count of  the  losses  in  the  motor  and  is  repre- 
sented by  /„.     This  is  called  the  no-load  current.     To  over- 
come the  back  e.m.f.  of  the  stator  Er,  we  must  apply  an  equal 
and  opposite  e.m.f.     This  is  represented  by  E9.     In  addition  to 
this,  the  applied  e.m.f.  would  have  a  component  in  phase  with 
the   current   to   overcome   the  ohmic  drop.     The  construction 
would  be  the  same  as  in  the  case  of  the  transformer  (see  Fig. 
137),  and  it  is  unnecessary  to  complicate  the  diagram  by  intro- 
ducing it. 

258.  Full-load  Diagrams. — As  soon  as  we  apply  a  load  to  the 
motor,  the  rotor  slows  down.  The  rotor  bars  therefore  cut  the 
revolving  magnetic  field  inducing  an  e.m.f.  in  them  and  a  cur- 
rent flows.  This  current  will  lag  somewhat  behind  the  rotor 
e.m.f.  The  lag,  however,  will  not  be  great,  since  the  frequency 
in  the  rotor  will  be  low.  The  rotor  current  may  be  represented 
by  the  vector  Ir  (see  Fig.  204).  As  in  the  case  of  the  trans- 
former, the  resultant  of  the  stator  and  the  rotor  current  must 


THE  INDUCTION  MOTOR 


273 


always  be  equal  to  the  no-load  current  and  this  latter  is  very 
nearly  constant.  The  magnetizing  current  may  therefore  be  re- 
presented by  In  as  before.  The  stator  current  will  then  be 
represented  by  Is,  whose  magnitude  and  direction  are  such  that 
the  resultant  of  7S  and  Ir  is  /„.  The  stator  current  of  the  motor 
under  load  does  not  lag  nearly  so  much  as  in  the  unloaded  motor. 
In  other  words,  the  power  factor  is  better. 

259.  Diagram  Representing  the  Conditions  at  Start.— If  full 
voltage  be  applied  to  the  stator  of  an  induction  motor  while  the 
rotor  is  at  rest,  the  e.m.f .  induced  in  the  rotor  is  of  course  large 
since  the  rotating  magnetic  field  is  moving  at  full  speed  while  the 
rotor  is  at  rest.  The  rotor  current  is  therefore  large.  The 
frequency  in  the  rotor  is  the  same  as  the  line  frequency.  Hence 


FIG.  204. 


the  lag  of  the  rotor  current  will  be  large,  and  the  current  will  be 
kept  from  becoming  very  great  on  account  of  the  large  reactance. 
The  diagram  of  the  motor  during  starting  is  shown  in  Fig.  205. 
The  large  lag  of  the  rotor  current  results  in  a  corresponding  lag 
of  the  stator  current  and  the  power  factor  of  the  machine 
is  low. 

260.  The  Circle  Diagram. — If  a  careful  test  is  made  of  an 
induction  motor  under  loads  varying  from  zero  to  such  a  load 
that  the  motor  is  unable  to  start,  the  results  may  be  embodied  in 
a  diagram  similar  to  that  of  Fig.  206.  The  voltage  is  kept  con- 
stant and  the  amperage  and  wattage  measured  for  each  load. 
The  power  factor,  and  the  angle  of  lag  can  be  readily  computed 
from  the  above  data.  Thus  the  angle  of  lag  at  no  load  may  be 
laid  off  as  EaOA  and  the  value  of  the  no-load  current  may  be 

18 


274      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

represented  by  the  length  OA.  Similarly  at  full-load  the  angle  of 
lag  may  be  EaOB  and  the  magnitude  of  the  current  may  be  OB. 
At  start  the  lag  is  represented  by  the  angle  ESOD  and  the 
current  by  OD.  At  no  load  we  may  take  the  rotor  current  as 
being  zero.  At  full  load  (assuming  that  the  motor  is  wound 
with  a  one  to  one  ratio)  it  will  be  AB  and  at  start  AD. 

If  the  work  is  carefully  done  it  will  be  found  that  all  points 
thus  taken  lie  approximately  upon  a  circle  having  as  diameter 
the  line  AG  parallel  to  OF.  The  proof  of  this  fact  while  not  dif- 
ficult, lies  outside  the  scope  of  this  work.  In  determining  the 
circle  in  practice,  usually  only  two  points  are  taken,  those  for 
no  load  and  for  the  starting  condition.  The  values  for  the 
starting  condition  are  usually  determined  at  a  reduced  voltage 
and  the  quantities  multiplied  by  the  proper  factors  to  give  full 


FIG.  206. 

voltage  values.  Thus,  but  little  power  is  required  in  the  test 
of  the  motor. 

Two  important  characteristics  of  the  motor  may  be  at  once 
determined  from  the  diagram.  The  maximum  power  factor  of 
the  motor  will  be  attained  at  such  a  load  that  the  current  vector 
drawn  from  0  is  just  tangent  to  the  circle,  since  then  the  angle  of 
lag  will  be  a  minimum.  The  maximum  input  to  the  motor  will 
be  at  such  a  load  that  the  current  vector  is  represented  by  OC. 
The  power  component  of  the  current  is  the  projection  of  the 
current  vector  upon  the  voltage  vector  OE8  and  this  will  ob- 
viously be  a  maximum  for  the  point  shown.  The  maximum 
output  of  the  motor  may  be  determined  approximately  if  the 
efficiency  is  known. 

By  simple  additions  to  the  circle  diagram  one  can  readily 
determine  the  efficiency,  slip,  torque,  starting  torque  and  other 
characteristics  of  the  motor.  However,  these  will  not  be  taken 
up  here. 


THE  INDUCTION  MOTOR 


275 


261.  Starting  Devices  for  Squirrel-cage  Motors. — Squirrel- 
cage  induction  motors  of  5  hp.  and  less  are  usually  started  by 
connecting  them  directly  to  the  line.  A  double-throw  switch 
should  preferably  be  used  with  either  no  fuses  at  all  or  large  fuses 
connected  to  the  starting  clips,  and  smaller  fuses  connected  to  the 
running  clips.  This  is  done  in  order  that  the  great  rush  of 
current  at  the  start  may  not  blow  the  fuses.  The  switch  should 
be  provided  with  a  spring  so  that  it  is  impossible  to  leave  it  in 
the  starting  position. 


ifflm 


FIG.  207. 


FIG.  208. 


In  the  case  of  large  motors,  it  is  customary  to  provide  some 
form  of  device  to  reduce  the  pressure  applied  to  the  terminals  of 
the  motor  during  the  starting  period.  This  is  done  more  to 
protect  the  connected  apparatus  against  the  danger  of  too  rapid 
acceleration,  and  to  lower  the  line  current  rather  than  to  protect 
the  motor.  The  latter  would  not  be  at  all  injured  by  being 
directly  connected  to  the  line.  The  inductance  of  the  motor  is 
such  that  only  from  five  to  eight  times  normal  current  would  flow, 


276      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

and  acceleration  would  be  so  rapid  that  no  serious  heating  would 
take  place  during  starting. 

262.  The  Auto -starter. — Figure  207  shows  the  external 
appearance  of  an  auto-starter  or  compensator  and  Fig.  208 
illustrates  the  same  starter  with  the  cover  and  oil  well  removed. 
The  connections  are  shown  in  Fig.  209.  The  apparatus  contains 
a  three-phase  transformer,  having  three  legs  upon  which  the  coils 
are  wound.  The  three  coils  are  star  connected  and  each  coil  is 
provided  with  three  taps  so  that  three  different  voltages  are 
available.  The  sliding  contacts  in  the  middle  row  are  mounted 
on  a  drum.  This  can  be  rotated  through  a  small  angle  so  that 
contact  can  be  established  between  the  middle  row  and  either 
the  top  or  the  bottom  row.  When  the  handle  is  thrown  to  the 


FIG.  209. 

starting  position  the  three  terminals  of  the  auto-transformer  are 
connected  to  the  line  wires  back  of  the  fuses,  and  the  wires  leading 
to  the  motor  are  connected  to  the  three  taps  on  the  transformer. 
When  the  motor  has  attained  nearly  full  speed  the  handle  is 
thrown  to  the  running  position.  This  disconnects  the  auto- 
transformer  from  the  line,  and  connects  the  motor  terminals 
directly  to  the  line  through  the  fuses. 

Generally  only  one  starting  position  is  provided.  This  is  in 
marked  contrast  to  continuous-current  practice  in  which  pro- 
vision is  made  for  cutting  out  the  starting  resistance  very  gradu- 
ally. Two  things  make  this  possible:  the  high  reactance  of  the 
induction  motor  which  prevents  great  rushes  of  current,  and  the 
fact  that  the  speed  depends  primarily  upon  the  frequency.  The 
motor  will  therefore  attain  practically  full  speed  upon  the 


THE  INDUCTION  MOTOR 


277 


reduced  starting  voltage  and  may  then  be  thrown  directly  upon 
the  line. 

Three  sets  of  starting  taps  are  provided  in  order  that  the  volt- 
age applied  at  start  may  be  made  as  low  as  possible  and  still 
start  the  load.  The  starting  torque  of  an  induction  motor  is 
proportional  to  the  square  of  the  voltage.  The  starting  torque 
with  full  voltage  applied  is  usually  from  150  to  200  per  cent,  of 
full-load  torque.  Taking  the  larger  figure  as  applying  to  a 
particular  motor,  it  will  be  seen 
that  if  one-half  of  the  line  volt- 
age is  applied  the  torque  will  be 
reduced  to  one-fourth  of  its 
maximum  value  or  50  per  cent, 
of  full-load  torque.  A  voltage 
of  70.7  per  cent,  of  normal  would 
give  full-load  torque.  The  three 
voltages  supplied  are  about  60, 
75,  and  90  per  cent,  of  line 
voltage. 

Auto-starters  or  compensators 
as  they  are  sometimes  called, 
are  frequently  equipped  with  no- 
voltage  release  and  occasionally 
with  overload  release  as  well.  In 
starters  for  2200  volts  or  more, 
the  overload  release  is  practically 
always  incorporated  with  the 
starting  switch. 

263.  Resistance  Starters  for 
Squirrel-cage  Motors. — A  lower 
voltage  for  starting  an  induction 
motor  may  also  be  obtained  by 
inserting  resistors  in  the  three  lines  supplying  the  motor.  A 
starter  of  this  type  is  shown  in  Fig.  210.  Such  starters  are  some- 
what cheaper  to  construct  and  are  simpler  to  repair  than  the 
auto-starter  type.  They  are  not  so  efficient  since  there  is  a 
loss  in  the  resistors,  but  this  is  a  very  small  matter  except  in 
the  case  of  large  motors  which  are  frequently  started.  Central 
stations  frequently  object  to  this  form  of  starter  on  the  plea  that 
a  large  current  is  taken  from  the  line,  and  that  therefore  the 
starting  of  the  motor  interferes  with  the  regulation  of  the  line. 


FIG.  210. 


278      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

Undoubtedly  more  current  is  taken  although  the  difference  is  not 
great,  particularly  in  the  case  of  a  heavily  loaded  motor  where 
perhaps  90  per  cent,  of  full  voltage  is  required  in  any  case.  The 
amount  of  wattless  current,  however,  is  the  same  in  the  two  types, 
and  it  is  principally  the  wattless  current  which  interferes  with  the 
line  regulation.  Tests  show  no  appreciable  difference  in  the  line 
disturbance  produced  by  the  two  types. 

264.  Star-delta   Starters. — Some  motors  may   be  started  by 
connecting  the  stator  windings  in  star,  to  start;  and  in  delta  for 
running.     This  means  that  during  starting  we  have  impressed 
across  each  winding  1  -f-  \/3  or  57.7  per  cent,  of  normal  voltage. 
Since  the  starting  torque  varies  as  the  square  of  the   applied 
voltage,  it  will  be  seen  that  the  starting  torque  will  be  only  one- 
third  of  the  maximum  which  the  motor  can  develop.     This  in 
many  cases  will  be  too  small,  and  since  there  is  no  possibility  of 
an  intermediate  step,  it  constitutes  an  objection  to  this  method. 
When  the  starting  load  is  light  or  may  be  made  so  without  great 
inconvenience,  this  is  an  excellent  method  of  starting. 

265.  Starters  for  Motors  with  Wound  Rotors. — In  starting 
these  motors  full  voltage  is  applied  to  the  stator  and  a  three-phase 
resistor  is  connected  to  the  three  slip  rings.     This  cuts  down  the 
current  in  the  rotor,  and  consequently. that  in  the  stator.     At  the 
same  time,  the  current  and  the  voltage  are  brought  more  nearly 
in  phase  and  so  the  starting  torque  is  improved.     Such  a  motor 
will  therefore  develop  more  torque  and  at  the  same  time  take  less 
current  from  the  line  than  a  corresponding  squirrel-cage  machine. 
It  is  therefore  to  be  preferred  when  frequent  stopping  and  starting 
are  required.     The  efficiency  is  usually  a  little  greater  than  that  of 
a  squirrel-cage  machine,  particularly  in  the  larger  sizes,  but  the 
power  factor  is  materially  lower  and  the  motor  is  more  costly. 
The  squirrel-cage*  machine  is  to  be  preferred  in  most  cases.     More 
detailed  information  will  be  found  under  Art.  270. 

266.  Adjustable-speed     Induction    Motors. — The    induction 
motor  has  many  advantages  over  the  continuous-current  motor, 
such  as  simplicity  and  durability,  but  for  adjustable-speed  work 
it  is  at  a  serious  disadvantage.     This  arises  primarily  from  the  fact 
that  the  speed  of  an  induction  motor  is  dependent  upon   the 
frequency,  while  that  of  a  direct-current  motor  depends  upon  the 
voltage  or  what  is  equivalent,  upon  the  flux  passing  through  the 
armature.     It  is  obviously  easy  to  change  the  voltage  or  the  flux, 
but  to  change  the  frequency  presents  great  difficulties. 


THE  INDUCTION  MOTOR  279 

267.  Changing  the  Number  of  Poles. — It  is  possible  to  make 
one  change  which  is  equivalent  to  varying  the  frequency,  namely, 
changing  the  number  of  poles.     Thus  a  certain  stator  may  be 
provided  with  two  entirely  distinct  windings,  one  arranged  for 
say  twelve  poles  and  the  other  for  eight.     Operated  on  60  cycles, 
the  first  would  give  a  synchronous  speed  of  600  r.p.m.  and  the 
latter  of  900.     If  the  rotor  were  of  the  squirrel-cage   type,   it 
would  serve  equally  well  for  both  stator  windings.     If  a  wound 
rotor  were  used,  it  would  be  necessary  to  provide  it  as  well  with 
two  windings  and  consequently  with  five  slip  rings,  one  ring 
being  common  to   the   two    windings.     This   method   gives    a 
reasonably  good  motor  with  two  speed  changes,  but  it  involves  the 
use  of  a  large  stator  to  carry  the  two  windings  and  the  machine 
will  have  slightly  poorer  characteristics  than  a  standard  motor. 

There  is  one  special  form  of  winding  which  can  be  applied  in 
such  a  manner  that  it  is  possible  to  double  the  number  of  poles 
merely  by  changing  the  points  of  connection  to  the  winding  and  at 
the  same  time  connecting  together  three  points  on  the  winding. 
This  gives  us  two  speeds  with  a  single  winding,  but  the  speeds 
must  be  in  the  ratio  of  two  to  one.  The  characteristics  of  the 
motor  also  suffer  somewhat. 

268.  Connection  in  Cascade  or  Concatenation. — Imagine  an 
induction  motor  in  which  the  stator  and  the  rotor  have  the  same 
number  of  turns.     If  the  motor  is  at  rest  with  voltage  applied  to 
the  stator,  it  will  act  as  a  transformer.     The  voltage  at  the  slip 
rings  will  be  the  same  as  that  of  the  line,  and  the  frequency  will 
also  be  the  same.     If  resistors  are  connected  to  the  three  slip 
rings,  and  the  load  and  the  resistance  are  so  adjusted  that  the 
motor  is  operating  at  half  of  synchronous  speed,  the  rotor  con- 
ductors will  be  moving  half  as  fast  as  the  flux  and  the  voltage  and 
frequency  at  the  rotor  slip  rings  will  be  half  as  great  as  when  the 
motor  was  at  rest.     The  power  wasted  in  the  resistors  connected 
to  the  three  slip  rings  will  be  nearly  half  of  that  supplied  to  the 
stator.     By  connecting  another  motor  of  the  same  capacity  and 
number  of  poles  both  mechanically  and  electrically  to  the  first 
one,  this  power  may  be  used.     The  connection  is  shown  in  Fig. 
211.     The  mechanical  connection  is  best  made  if  possible    by 
mounting  the  rotors  on  the  same  shaft  and  the  electrical  connec- 
tion is  made  by  connecting  the  slip  rings  of  the  first  motor  to  the 
stator  of  the  second.     The  second  motor  may  have  either   a 
squirrel  cage  or  a  wound  rotor.     As  the  power  supplied  from  the 


280      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

first  motor  is  of  half  frequency  and  half  voltage  it  will  be  correct 
to  drive  the  second  motor  at  the  same  speed  as  the  first.  The  first 
machine  will  be  acting  partly  as  a  motor  and  partly  as  a  frequency 
changer.  Either  motor  or  both  of  them  may  be  connected 
directly  to  the  line  in  the  usual  way  in  which  case  they  will  run  at 
full  speed,  i.e.,  double  the  speed  in  cascade. 

The  motors  need  not,  however,  have  the  same  number  of 
poles.  Thus  the  first  may  have  four  and  the  second  six  poles. 
The  synchronous  speed  of  the  first  one  alone  on  60  cycles  would 
be  1800  r.p.m.,  and  that  of  the  second  alone  1200  r.p.m.  The 
two  connected  in  cascade  would  have  a  speed  corresponding  to 
the  sum  of  the  two  sets  of  poles,  in  this  case  ten  poles  or  720 
r.p.m.  Thus  with  the  two  motors  three  speeds  would  be  avail- 
able. The  same  principle  may  be  applied  to  more  than  two 
motors,  although  it  is  rarely  done.  This  method  gives  quite 
good  results,  but  it  is  somewhat  expensive. 


FIG.  211.   . 

269.  Induction  Motors  with  Commutators. — A  commutator 
is  a  frequency  changer.  Thus  in  a  continuous-current  motor  it 
changes  a  continuous  current  (zero  frequency)  into  an  alternating 
current  or  vice  versa.  In  a  similar  manner  it  may  change 
an  alternating  current  from  one  frequency  to  another.  If  one 
places,  in  a  stator  of  the  usual  type,  a  rotor  having  a  winding  and 
a  commutator  identical  with  those  of  a  direct-current  machine, 
the  frequency  at  the  brushes  will  always  be  that  of  the  line,  no 
matter  what  the  speed  of  the  rotor.  This  being  so,  it  is  possible 
to  impress  different  voltages  upon  the  brushes  by  means  of  a 
variable  ratio  transformer  and  in  this  manner  change  the  speed. 
The  speed  can  therefore  be  adjusted  through  a  considerable 
range  both  above  and  below  synchronism  without  the  use  of 
resistors  and  consequently  with  high  efficiency. 

Such  motors  are  expensive  and  present  difficulties  from  the 
standpoint  of  commutation.  They  are  occasionally  built  for 
special  requirements,  usually  in  large  sizes. 


THE  INDUCTION  MOTOR 


281 


Torque 
100% 


FlG   212 


\ 


250% 

E 


270.  The  Wound-rotor  Machine  for  Adjustable  Speed  Work. 
—  A  number  of  speed-torque  curves  of  a  wound-rotor  induction 
motor  are  shown  in  Fig.  212.  The  torque  plotted  is  that  de- 
veloped in  the  rotor.  The  torque  actually  applied  to  the  load 
is  slightly  less  on  account  of  bearing  friction.  Curve  A  shows 
the  torque  at  different  speeds  when  the  external  resistance  in  the 
rotor  is  zero.  As  previously  explained  (see  Art.  251),  the  torque 
at  starting  is  small  on  account  of  the  great  lag  of  the  current 
behind  the  e.m.f.,  and  the  consequent  fact  that  the  current  in 
the  rotor,  is  displaced  in  position  from  the  flux.  As  the  motor 
speeds  up,  the  current  decreases  but  the  torque  increases  to  a 
maximum  value  of  OD.  This  is  attained  when  the  motor  has 
nearly  reached  synchronism. 
Beyond  this  point  the  torque 
rapidly  decreases  with  in- 
creased speed  until  it  reaches 
zero  at  synchronism.  If 
driven  above  this  speed  the 
torque  reverses  and  the  ma- 
chine becomes  a  generator. 

With  a  low  resistance  con- 
nected  to  the  slip  rings  the 
speed-  torque  curve  would  be 
represented  by  such  a  curve 
as  B.  This  would  also  correspond  to  an  average  speed-torque 
curve  for  a  squirrel-cage  motor,  as  such  motors  are  purposely 
built  with  a  moderate  rotor  resistance  in  order  that  the  torque 
at  start  may  be  sufficient  for  average  conditions.  The  inser- 
tion of  still  more  resistance  would  give  such  curves  as  C,  D,  E, 
andF. 

It  will  be  noted  that  the  maximum  torque  that  can  be  obtained 
is  the  same  no  matter  what  the  speed,  or  to  state  it  in  different 
words,  the  motor  can  carry  this  maximum  torque  at  any  speed 
between  zero  and  a  speed  perhaps  10  per  cent,  below  synchronous 
speed,  provided  the  rotor  resistance  is  properly  adjusted.  The 
same  is  true  of  any  smaller  torque.  Thus,  full-load  torque  could 
be  obtained  at  any  of  the  speeds  given  by  the  intersection  of  the 
speed  curves  with  the  line  representing  100  per  cent,  torque. 
With  a  given  torque,  then,  the  speed  may  be  adjusted  through  a 
considerable  range. 

The  motor  is,  however,  not  an  adjustable-speed  motor  in  the 


282      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

sense  that  the  term  is  usually  employed,  since  if  the  resistance 
were  so  adjusted  that  the  motor  operated  at  half  speed  with  full- 
load  torque  it  would  run  at  nearly  full  speed  with  no  load,  at 
about  three-fourths  speed  with  25  per  cent,  of  full-load  torque, 
etc.  In  other  words,  the  speed  regulation  of  the  motor  is  poor 
when  there  is  considerable  resistance  in  the  rotor  circuit. 

The  efficiency  is  also  low.  Thus -if  the  motor  is  operating 
at  half  speed,  practically  half  of  the  power  supplied  to  the 
stator  is  wasted  in  the  resistance  of  the  rotor  and  external 
resistors.  The  efficiency  will  therefore  be  less  than  50  per  cent. 
If  the  speed  were  reduced  to  25  per  cent,  of  normal,  the  efficiency 
would  be  less  than  25  per  cent.,  etc.  On  account  of  these  facts, 
this  method  of  speed  regulation  is  not  used  to  any  great  extent. 

271.  The  Single-phase  Induction  Motor. — A  complete  treat- 
ment of  the  single-phase  induction  motor  involves  considerable 
difficulty  and  will  not  be  attempted  here.     However,  some  of  the 
principal  facts  in  connection  with  it  should  be  stated. 

If  a  two-phase  motor  is  operating  without  load  and  one  of  the 
phases  is  opened,  the  motor  will  continue  to  rotate  and  the  only 
noticeable  change  will  be  a  slight  difference  in  the  hum  of  the 
motor.  If  an  ammeter  is  inserted  in  the  phase  that  is  left  closed, 
it  will  be  found  that  the  current  per  phase  operating  single  phase 
is  about  double  that  operating  two  phase.  If  the  same  ex- 
periment be  made  with  a  three-phase  motor  by  opening  one  of 
the  three  leads,  it  will  be  found  that  the  current  changes  in  the 
ratio  of  1  to  \/3,  or  it  increases  73  per  cent. 

272.  Rotating  Magnetic  Field. — If  with  the  motor  operating 
single  phase  at  no  load  one  investigates  the  magnetic  field  by  suit- 
able experiments,  it  will  be  found  that  there  is  a  rotating  mag- 
netic field  just  as  in  the  case  of  the  polyphase  motor.     If  the 
motor  is  loaded  it  will  be  found  that  the  field  is  rotating  but  that 
it  is  stronger  in  the  direction  of  the  axis  of  the  primary  winding 
than  it  is  in  a  direction  at  90°  to  this  axis.     The  difference  will 
be  in  the  neighborhood  of  5  to  10  per  cent.     If  the  motor  is  at 
rest,  the  field  does  not  rotate  but  merely  pulsates. 

We  may  gain  a  rough  idea  of  the  manner  in  which  this  rotating 
magnetic  field  is  set  up  in  the  following  way:  The  rotor  is 
highly  inductive,  and  like  any  inductive  circuit  it  resists  strongly 
any  attempt  to  change  the  flux  passing  through  it.  Imagine  that 
at  a  certain  instant  the  stator  current  is  a  maximum  and  that  flux 
is  passing  through  the  stator  coil  and  through  the  rotor  in  line 


THE  INDUCTION  MOTOR 


283 


with  the  axis  of  the  stator  coil  (see  Fig.  213).  The  rotation 
is  in  a  clockwise  direction.  If  there  were  no  winding  on 
the  rotor  the  flux  would  drop  to  zero  when  the  rotor  had 
moved  through  an  angle  of  90  electrical  degrees.  The  moment, 
however,  that  the  flux  begins  to  decrease  along  this  axis  of 
the  rotor,  a  powerful  current  is  induced  in  the  rotor  wind- 
ing. This  current,  in  accordance  with  Lentzrs  law,  resists  the 
change  of  flux,  and  is  powerful  enough  to  prevent  much  change. 
The  result  is  that  when  the  stator  current  drops  to  zero  and  the 
rotor  has  turned  through  an  angle  of  90  electrical  degrees,  as 
shown  in  Fig.  214,  there  is  a  current  in  the  rotor  bars  at  such  a 
position  on  the  rotor  surface  as  to  magnetize  it  along  an  axis  90° 


FIG.  213. 


FIG.  214. 


from  the  axis  of  the  stator  coil.  The  flux  through  the  rotor  has 
changed  slightly  in  order  that  this  current  may  be  generated, 
but  the  change  is  small.  It  may  then  be  said  roughly  that  the 
flux  along  the  axis  of  the  stator  coil  is  provided  by  the  current  in 
the  stator.  That  flux  which  is  along  an  axis  at  right  angles  to 
the  stator  coil  is  due  to  current  in  the  rotor. 

Similar  considerations  will  show  that  when  the  rotor  turns 
further  the  flux  through  it  will  again  tend  to  increase.  The  cur- 
rents in  the  rotor  bars  will  so  arrange  themselves  as  to  oppose 
the  slight  change,  and  when  the  current  in  the  stator  winding  is 
again  a  maximum,  the  rotor  currents  will  be  in  such  a  position 
as  to  oppose  the  stator  curent.  The  stator  current  will  there- 
fore have  to  be  larger  than  if  the  rotor  current  were  not  present, 


284      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

that  is,  larger  than  would  be  the  case  in  a  polyphase  motor. 
As  has  been  stated,  in  the  case  of  a  two-phase  motor  it  would 
be  doubled. 

273.  Starting  Torque. — If  single-phase  current  be  applied  to 
one  phase  of  a  polyphase  motor  when  the  latter  is  at  rest,  abso- 
lutely no  starting  torque  will  be  developed.     If  the  motor  be 
given  an  initial  start  in  either  direction  by  pulling  the  belt  or 
otherwise,  the  motor  will  develop  a  small  torque  and  will  ac- 
celerate to  nearly  synchronism,  in  the  direction  in  which  the  im- 
pulse was  given.     That  there  would  be  no  starting  torque  and 
that  the  motor  would  operate  equally  well  in  either  direction 
might  have  been  inferred  from  the  fact  that  the  motor  is  sym- 
metrical.    There  is  absolutely  no  reason  why  it  should  rotate  in 
one  direction  rather  than  in  the  other.     A  mechanical  structure 
exhibiting  the  same  peculiarity  is  the  familiar  two-cycle  gasoline 
engine  with  the  spark  set  on  dead  center. 

274.  Split -phase  Starters. — One  method  by  which  the  single- 
phase  induction  motor  may  be  given  a  small  starting  torque  is 


Inductance           Resistance 

\M$&MtfttLr^WV\/\/\s 

FIG.  215. 

illustrated  in  Fig.  215.  The  winding  is  that  of  a  standard  three- 
phase  motor.  For  starting,  two  leads  are  connected  directly  to 
the  line.  A  reactor  and  a  resistor  connected  in  series  are  also 
connected  across  the  line.  The  third  lead  is  connected  to  the 
junction  of  the  resistor  and  the  reactor.  The  currents  in  the 
three  circuits  will  differ  in  phase,  and  an  imperfect  rotating 
magnetic  field  will  be  set  up,  After  the  motor  is  up  to  speed,  two 
of  the  leads  will  be  connected  to  the  two  line  wires,  and  the  third 
lead  will  be  left  on  open  circuit.  The  resistor  and  reactor  are,  of 
course,  disconnected. 


THE  INDUCTION  MOTOR  285 

The  torque  produced  in  this  manner  is  feeble,  and  it  is  generally 
necessary  to  make  provision  so  that  the  motor  may  be  started 
without  load.  This  may  be  done  by  means  of  a  centrifugal  clutch 
which  takes  hold  of  the  pulley  when  the  motor  has  nearly  reached 
synchronous  speed. 

275.  Starting  as  a  Repulsion  Motor. — A  great  many  single- 
phase  motors  are  built  to  start  as  repulsion  motors  but  operate 
after  starting   as  induction   motors.     The  rotor   resembles  the 
armature  of  a  continuous-current  machine,  and  is  provided  with  a 
commutator  and  brushes.     The  brushes  are  short-circuited.     If 
the  brushes  are  given  a  lead  in  either  direction,  a   powerful 
torque  will  be  developed  tending  to  turn  the  rotor  in  that  direc- 
tion.    When  the  motor  has  nearly  reached  synchronous  speed  a 
centrifugal  device  acts  to  remove  the  brushes  from  the  commuta- 
tor and  at  the  same  time  to  short-circuit  all  of  the  bars  of  the 
commutator.     The  motor  then  continues  to  run  as  a  squirrel-cage 
induction  motor.     The  action  of  the  repulsion  motor  is  described 
in  more  detail  in  the  next  chapter.     (See  Art.  300.) 

276.  Synchronous  Motors  versus  Polyphase  Induction  Motors. 
— The  following   is   a   brief   comparison    of   the  points    to   be 
considered  in  making  a  choice  between  the  above  two  types  of 
motors. 

Efficiency. — The  synchronous  motor  should  run  a  little  higher 
in  efficiency  since  the  power  factor  may  be  made  better  and, 
therefore,  the  I2R  losses  in  the  stator  are  less.  The  loss  in  the 
field  should  also  be  less  than  that  in  the  rotor  of  a  squirrel-cage 
induction  motor  since  the  resistance  of  the  latter  is  necessarily 
high  to  get  the  requisite  starting  torque.  This  advantage  is 
partially  offset  by  the  fact  that  the  field  current  of  the  synchron- 
ous motor  is  usually  generated  in  a  small  and  comparatively  in- 
efficient machine. 

277.  Power  Factor. — The  synchronous  machine  has  here  ^  a 
great  advantage.     If  the  wave  shapes  of  the  line  voltage  and  the 
machine  voltage  are  the  same,  the  power  factor  can  always  be 
made  unity.     It  is  also  always  possible  to  make  the  current  lead 
the  e.m.f.  by  overexciting  the  field.     This  leading  current  maybe 
of  great  value  as  a  means  of  offsetting  lagging  current  due  to  the 
presence  of  induction  motors  or  other  causes.     The  synchronous 
machine  also  greatly  improves  the  regulation  of  the  line  by  taking 
a  lagging  or  leading  current  as  may  be  required  to  correct  the 
voltage  variations. 


286      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

278.  Speed  Regulation. — Under  full  load  a  small  induction 
motor  may  slow  down  as  much  as  10  per  cent,  and  a  large  one 
perhaps  as  little  as  1  per  cent.     This  amount  of  variation  in  speed 
is  usually  not  objectionable.     In  the  case  of  the  synchronous 
machine,  however,  the  speed  regulation  is  perfect,  that  is,  the 
motor  does  not  slow  down  at  all  under  load.     Under  certain 
conditions  this  may  be  advantageous. 

279.  Overload  Capacity. — It  must  not  be  supposed  that  a 
synchronous  motor  is  readily  pulled  out  of  step  and  that  conse- 
quently they  are  incapable  of  carrying  heavy  overloads.     As  a 
matter  of  fact,  almost  any  synchronous  motor  will  carry  from  two 
to  three  times  its  rated  load  without  difficulty.     Approximately 
the  same  figures  apply  to  the  induction  motor  and  there  is,  there- 
fore, little  to  choose  between  the  two  in  this  respect. 

280.  Hunting. — The  induction  motor  causes  no  trouble  by 
hunting.     The   synchronous   motor   may   do   so.     However,   if 
provided  with  a  squirrel-cage  winding  in  the  pole  faces  or  with 
special  grids  on  the  poles  there  should  be  no  serious  hunting 
under  usual  commercial  conditions. 

281.  Starting  Torque. — A   wound-rotor  induction    motor  of 
fair  size  will  develop  100  per  cent,  starting  torque  with  about  110 
per  cent,  of  full-load  current,  or  a  maximum  of  about  225  per 
cent,  of  full-load  torque  with  about  270  per  cent,  of  full-load 
current.     The  squirrel-cage  motor  will  develop  a  maximum  of 
200  per  cent,  torque  with  about  600  per  cent,  of  full-load  current. 
A  synchronous  motor  will  develop  a  maximum  torque  of  per- 
haps 125  per  cent,  with  500  per  cent,  of  full-load  current.     These 
figures  vary  greatly,  however,  in  different  motors. 

It  will  be  seen  that  the  synchronous  motor  is  not  far  behind  the 
squirrel-cage  motor  in  starting  torque.  However,  some  difficulty 
may  be  experienced  with  heavy  loads  at  the  instant  when  the 
current  is  passed  through  the  fields  and  the  motor  should  drop 
into  step.  Up  to  this  time,  it  has  been  acting  as  an  induction 
motor  and  it  is  necessary  that  it  accelerate  quickly  so  that  it  may 
fall  into  step  as  a  synchronous  motor.  Whether  or  not  it  will  be 
able  to  do  this  depends  more  upon  the  inertia  of  the  connected 
load  than  upon  the  torque  required  to  maintain  rotation. 

282.  Air-gap  Clearance. — The  synchronous  motor  has  a  con- 
siderable advantage  in  the  fact  that  the  air-gap   clearance  is 
several  times  as  great  as  in  the  induction  motor.     There  is, 


THE  INDUCTION  MOTOR  287 

therefore,  less  danger  that  the  bearings  may  wear  to  such  an 
extent  that  the  rotor  will  strike  upon  the  stator. 

283.  Attention  Required. — About  all  the  care  required  by  the 
induction  motor  is  keeping  the  machine  clean  and  replenishing 
the  oil  in  the  bearings  occasionally.     In  the  case  of  the  synchron- 
ous motor  a  new  factor  is  added — the  adjustment  of  the  power 
factor  by  means  of  the  field  current.     To  check  this  adjustment, 
instruments  are  usually  used  with  the  motor.     The  operation  of 
the  motor  therefore  requires  a  slightly  higher  grade  of  labor,  and 
much  damage  could  be  done  by  a  careless  or  ignorant  attendant. 

284.  Slow-speed  Motors. — An  induction  motor  of  moderate 
size,  say  200  hp.  operating  at  such  a  speed  as  240  r.p.m.  on  60- 
cycle  current,  is  a  very  poor  machine.     The  power  factor  is  low 
and  in  consequence  the  efficiency  suffers.     The  starting  torque 
is  also  likely  to  be  low.     These  difficulties  can  be  largely  avoided 
in  the  synchronous  motor  and  it  is  therefore  generally  preferred 
for  such  service. 

PROBLEMS 

103.  An  induction  motor  is  to  operate  on  60-cycle  current  and  have  a 
synchronous  speed  of  150  r.p.m.     How  many  poles  must  it  have? 

104.  How  many  poles  must  it  have  when  operating  on  25-cycle  current 
in  order  that  the  speed  may  be  the  same? 

106.  What  is  the  maximum  speed  that  a  60-cycle  induction  motor  may 
have?     A  25-cycle  motor? 

106.  A  six-pole  25-cycle  generator  is  driven  by  a  60-cycle  induction  motor. 
How  many  poles  must  the  latter  have,  allowing  a  small  amount  for  slip? 

107.  A  60-cycle,  eight-pole  induction  motor  is  operating  under  load  at  a 
speed  of  856  r.p.m.     What  is  the  slip ?     What  is  the  frequency  of  the  current 
in  the  rotor? 

108.  What  would  be  the  slip  and  the  rotor  frequency  at  a  speed  of  450 
r.p.m.? 

109.  An  induction  motor  when   connected  directly  across  a  440-volt 
circuit  develops  a  starting  torque  of  200  per  cent.     What  torque  will  it 
develop  when  started  by  means  of  a  compensator  if  the  terminal  voltage  of 
the  latter  is  220?     What  if  340  volts? 

110.  A  60-cycle  induction  motor  has  two  windings  upon  the  stator  giving 
respectively  ten  and  sixteen  poles.     What  will  be  the  respective  speeds  with 
the  two  windings? 

111.  Two  induction  motors  are  wound  with  ten  and  six  poles  respectively 
and  are  arranged  on  the  same  shaft  for  operation  in  cascade  on  a  60-cycle 
circuit.     What  are  the  possible  synchronous  speeds? 

112.  In  the  above  the  supply  voltage  is  440  volts,  three-phase.     The  ten- 
pole  motor  is  the  one  connected  to  the  line  and  is  provided  with  a  three-phase 
wound  rotor.    The  ratio  of  turns  in  the  stator  and  rotor  is  1  to  1.     What 


288      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

is  the  voltage  across  the  slip  rings  of  the  first  motor,  the  motor  being  at  rest 
and  the  rotor  circuit  open?  When  the  two  motors  are  connected  in  cascade 
as  above,  what  is  the  voltage  at  the  slip  rings?  What  is  the  frequency? 
Are  the  voltage  and  frequency  correct  for  the  second  motor  at  the  speed 
attained? 

113.  A  six-pole  induction  motor  operating  upon  a  60-cycle,  three-phase 
circuit  gave  the  following  results  upon  test:  Input,  22  kw.,  current  64  amp., 
voltage  220,  frequency  60  cycles.     What  was  the  power  factor?     What  was 
the  power  component  of  the  current?     The  wattless  current? 

114.  At  the  same  time  that  the  above  readings  were  taken,  the  readings 
on  a  Prony  brake  were  as  follows:  Length  of  arm  3  ft.,  net  weight  38  lb., 
speed  1150  r.p.m.     What  was  the  horse-power  output,  the  kilowatt  output, 
the  efficiency  and  the  slip?     What  was  the  loss  in  the  motor? 

115.  Assuming  the  same  efficiency,  power  factor  and  output  as  in  the 
above  problem,  what  would  be  the  current  taken  by  a  two-phase  motor 
operating  on  a  440-volt  circuit? 


CHAPTER  XIX 
THE  SINGLE-PHASE   COMMUTATOR  TYPE  MOTOR 

285.  Methods  of  Operating  Electric  Locomotives. — Within 
the  last  few  years  there  has  come  into  use  a  type  of  single-phase 
motor  designed  somewhat  along  the  lines  of  a  continuous-current 
motor.  This  motor  has  been  developed  with  the  primary  object 
of  adapting  it  to  the  requirements  of  railway  service.  As  has 
been  previously  explained,  in  practically  all  large  installations 
the  power  is  generated  as  alternating  current,  usually  three  phase. 
For  railway  operation,  this  is  frequently  converted  to  direct 
current  by  rotary  converters  or  by  other  suitable  means.  This 
involves  a  double  conversion,  since  the  pressure  must  first  be 
reduced  before  supplying  the  current  to  the  rotaries,  and  it  must 
then  be  changed  to  direct  current.  The  direct  current  is  usually 
supplied  at  pressures  approximating  600  volts,  and  since  it  is 
impracticable  to  transmit  current  at  this  potential  efficiently  to 
great  distances,  it  becomes  necessary  to  provide  rotary  converter 
sub-stations  at  distances  of  about  10  miles  apart.  Even  with  this 
spacing  the  cost  of  copper  for  efficient  operation  is  large,  and  since 
the  rotating  machinery  must  be  under  constant  supervision,  the 
operating  cost  is  high.  This  latter  charge  is  not  so  burdensome 
in  the  case  of  interurban  roads,  since  the  converter  stations  can 
usually  be  placed  at  points  at  which  it  would  be  necessary  in  any 
event  to  have  a  ticket  or  freight  agent.  In  the  case  of  trunk-line 
electrification,  this  solution  is  usually  impracticable.  By  using 
higher  voltages  on  the  trolley  wire  it  becomes  possible  to  space 
the  sub-stations  farther  apart,  thus  reducing  the  cost  of  attend- 
ance and  the  amount  of  copper  installed.  Direct-current  poten- 
tials as  high  as  2400  to  3000  volts  are  now  being  successfully 
used. 

Another  solution  is  to  mount  the  converting  machinery  on  the 
locomotive,  thus  avoiding  the  loss  in  transmission  and  part  of  the 
cost  of  attendance.  The  current  in  this  case  should  preferably 
be  supplied  as  high-voltage  single-phase  current,  and  may  be  con- 
verted either  to  continuous  current  or  to  three-phase  current. 
19  289 


290       PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

This  involves  considerable  complication,  and  the  added  weight 
on  the  locomotive  is  usually  a  serious  handicap,  unless  the  weight 
is  needed  for  traction. 

Three-phase  induction  motors  have  been  successfully  used  on 
electric  locomotives.  In  the  opinion  of  most  engineers,  however, 
their  field  of  usefulness  is  limited  on  account  of  the  constant-speed 
characteristics  of  this  type  of  motor.  It  is  true  that  by  adding 
somewhat  to  the  complication  of  the  apparatus  two,  three  or  more 
speeds  can  be  obtained.  Even  then  the  motor  still  lacks  the 
flexibility  of  the  series-wound  direct-current  motor.  It  is  the 
influence  of  these  facts  that  has  led  to  the  development  of  the 
single-phase  system. 

286.  The     Single -phase     System. — The     continuous-current 
motor  is  entirely  satisfactory  for  railway  work.     The  difficulty  is 
to  get  the  direct  current  to  it  without  great  loss  and  complication. 
The  three-phase  induction  motor  is  exceedingly  simple,  but  it  is 
handicapped  by  its  constant-speed  characteristics.     To  get  the 
three-phase  current  to  the  locomotive  requires  the  use  of  three 
conductors — the  track  and  two  overhead  wires.     This  leads  to 
some  complication,  particularly  in  terminal  yards. 

In  the  single-phase  system  the  power  may  be  generated  either 
as  single-  or  as  three-phase  current.  It  is  transmitted  at  high 
voltage  (usually  40,000  or  over),  and  is  stepped  down  by  means 
of  stationary  transformers  to  a  lower  voltage  (say  6600  volts) 
to  supply  the  overhead  conductor.  On  the  locomotive  or  car 
the  pressure  is  again  reduced  by  means  of  a  transformer  to 
about  200  volts.  There  is  no  moving  machinery  between  the 
generating  station  and  the  motors,  and  the  current  is  trans- 
mitted at  high  pressure  all  the  way  to  the  locomotive.  This 
should  therefore  lead  to  a  cheap  and  efficient  distributing  system. 
Unfortunately,  as  will  appear  from  the  following,  the  single- 
phase  motor  is  by  no  means  as  good  as  the  direct-current  motor. 
To  get  a  just  comparison  we  must  consider  each  case  on  its 
individual  merits  and  must  take  care  to  consider  the  systems 
as  a  whole  and  not  any  particular  element  alone. 

287.  Series-wound,  Commutator  Type,  Single-phase  Motor. 
— Consider  first  a  direct-current,  series-wound  motor.     If  the 
current  through  such  a  motor  is  reversed,  the  polarity  of  the 
fields  will  be  changed  at  the  same  time  that  the  current  is  re- 
versed through  the  armature.     The  torque  will,  therefore,  be 
exerted  in  the  same  direction  as  before.     If  it  is  assumed  that 


SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR 


291 


the  reversals  are  very  slow,  say  one  per  second,  the  principal 
point  of  difference  from  direct-current  operation  will  be  the  fact 
that  the  torque,  instead  of  being  constant,  will  vary  with  the 
time,  being  zero  at  the  instant  when  the  current  is  zero  and  a 
maximum  when  the  current  is  at  its  highest  value.  It  will  be 
apparent  that  if  the  average  torque  is  to  be  the  same  as  it  would 
be  if  a  direct  current  of,  say,  100  amp.  were  used,  the  effective 
value  of  the  slowly  alternating  current  must  also  be  100  amp. 
The  maximum  value  must,  however,  be  greater  than  this  in  the 
ratio  of  \/2  to  1,  or  141  amp.  The  I2R  loss  will  be  the  same  in 
the  two  cases.  The  commutation  will  be  more  difficult  in  the 
case  of  the  motor  on  the  slowly  alternating  current  since  this  is 
largely  determined  by  the  maximum  value  of  the  current. 


FIG.  216. 

288.  Heating. — If  an  attempt  were  made  to  operate  a  direct- 
current  series  motor  on  the  ordinary  commercial  frequency  of 
25  cycles,  three  serious  difficulties  would  be  encountered.     In 
the  first  place  the  motor  would  heat  excessively.    This  would  be 
due  to  the  eddy  currents  induced  in  the  solid  poles  and  yoke  of  the 
motor.     The  solid  core  would  act  like  the  short-circuited  second- 
ary of  a  transformer  having  one  secondary  turn.     Operation 
under  these  circumstances  would  be  impossible.     This  difficulty 
can,  however,  be  rather  easily  overcome  by  building  the  entire 
magnetic  circuit  of  laminated  iron. 

289.  Power  Factor. — The  second  difficulty  encountered  would 
be  that  the  power  factor  would  be  found  to  be  very  low.     To 
understand  this  fully,  it  will  be  necessary  to  construct  the  vector 


292      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

diagram  of  the  motor.  Consider  first  the  diagrammatic  repre- 
sentation of  a  series  motor  in  Fig.  216.  For  simplicity  this  is 
shown  as  a  two-pole  machine.  In  practice,  the  motors,  except 
in  the  smallest  sizes,  would  be  multipolar  and  would,  in  general, 
have  more  poles  than  a  corresponding  direct-current  machine. 
The  armature  is  shown  as  of  the  ring-wound  type.  This  is 
frequently  assumed  for  simplicity  in  drawing  diagrams  of  such 
machines.  In  practice,  the  ring-wound  armature  is  not  used 
for  this  purpose. 

290.  Generated  E.M.F. — Consider,  now,    that   the  armature 
is  rotating  in  a  constant  field.     A  difference  of  potential  will 
exist  between  the  points  on  the  commutator  at  which  the  brushes 
are  placed.     If  the  brushes  are  moved  from  this  position  the 
difference  of  potential  would  become  less,  reaching  zero  at  a 
position  90°  from  the  one  indicated. 

If,  instead  of  supplying  the  field  with  a  continuous  current,  it 
is  excited  by  means  of  an  alternating  current,  the  e.m.f .  at 
the  brushes  will  also  be  alternating.  The  frequency  will  be  the 
same  as  the  frequency  of  the  current  in  the  fields.  With  the 
field  flux  zero,  the  generated  e.m.f.  will  also  be  zero,  and  with 
the  flux  at  its  maximum,  the  e.m.f.  will  also  be  maximum. 
This  e.m.f.  will  therefore  be  in  phase  with  the  flux,  and  since  the 
flux  is  nearly  in  phase  with  the  current,  the  induced  e.m.f.  will 
be  nearly  in  phase  with  the  current  in  the  field.  If  it  were  de- 
sirable, an  alternating-current  generator  could  be  constructed 
in  this  way.  The  ordinary  construction  is,  however,  much 
cheaper,  except  possibly  in  the  case  of  machines  designed  for 
frequencies  of  10  cycles  per  second  or  less. 

291.  Induced    E.M.F. — The    conditions  are  different  in    the 
field.     The  only  induced  e.m.f.  present  will  be  that  due  to  the 
cutting  of  the  field  conductors  by  the  alternating  flux.     This 
induced  e.m.f.  will  be  90°  behind  the  current,  and  there  will 
also  be  a  component  of  applied  e.m.f.  in  phase  with  the  current 
to  overcome  the  resistance  of  the  windings. 

When  the  field  and  armature  are  connected  in  series  and 
the  machine  operated  as  a  motor,  the  conditions  in  the  field  will 
be  the  same  as  before.  The  induced  e.m.f.  in  the  armature 
now  becomes  the  back  e.m.f.  of  the  motor.  Moreover,  since 
the  armature  has  itself  reactance  and  resistance,  it  will  act  as  an 
inductive  circuit,  in  the  same  manner  as  the  field. 


SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR 


293 


292.  Vector  Diagram  of  Motor. — Figure  217  shows  the  vector 
diagram  of  the  motor.  If  the  vector  representing  the  current 
is  drawn  as  a  horizontal  line,  the  flux  will  be  nearly  in  the  same 
phase,  and  may  be  represented  without  serious  error  as  being 
exactly  in  the  same  phase.  The  line  marked  L/Jco,  is  drawn  to 
represent  the  e.m.f.  required  to  overcome  the  reactance  of  the 
field.  The  line  R/I,  is  the  e.m.f.  required  to  overcome  the 
resistance  of  the  field.  Similarly  L0/co  and  Ral  represent  the 
e.m.fs.  required  to  overcome  the  reactance  and  resistance  of  the 
armature.  In  addition  there  is  an  e.m.f.  required  to  overcome 
the  back  induced  e.m.f.  of  the  armature.  This  is  marked  Ea 
in  the  diagram.  The  total  e.m.f.  applied  to  the  motor  is  the 
vector  sum  of  these  five  e.m.fs.,  and  is  marked  E.  The  angle  of 
lag  of  the  current  behind  the  e.m.f.  is  the  angle  6  as  shown. 

Of  the  five  e.m.fs.,  the  two  due  to  the  inductance  of  the 


Lflu 


FIG.  217. 


armature  and  the  field,  and  the  two  due  to  the  resistance  of  the 
same  elements  are  proportional  to  the  current  flowing  in  the 
motor.  The  induced  e.m.f.  in  the  armature  Ea  is  directly  pro- 
portional to  the  flux  and  nearly  proportional  to  the  current.  It 
is,  however,  also  directly  proportional  to  the  speed  of  the  arma- 
ture. If  the  armature  is  at  rest  as  at  the  moment  of  starting, 
this  latter  e.m.f.  will  be  zero.  The  resultant  applied  e.m.f. 
will  then  be  represented  by  the  dotted  line  marked  EQ,  and  the 
power  factor  will  be  the  cosine  of  the  angle  00. 

293.  Changes  to  Improve  Power  Factor. — To  secure  a  good 
power  factor  with  a  motor  of  this  type,  two  conditions  are 
necessary;  the  back  induced  e.m.f.  Ea  must  be  made  as  great, 
relatively,  as  possible,  and  the  induced  e.m.fs.  in  the  field  and 
armature  must  be  reduced  as  much  as  possible.  It  might 
seem  that  the  power  factor  could  be  improved  by  increasing  Ral 
and  Rfl.  This  is,  of  course,  the  case,  but  it  would  be  only  at  the 


294      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

expense  of  the  efficiency,  since  these  two  multiplied  by  the 
current  represent  the  loss  in  the  resistance  of  the  machine. 

The  value  of  Ea  can  be  increased  by  increasing  the  flux,  the 
number  of  conductors  on  the  armature  or  by  increasing  the  speed. 
It  will  be  found  that  the  average  speed  of  single-phase  railway 
motors  is  higher  than  that  of  the  corresponding  continuous- 
current  motors.  Weakening  of  the  flux  reduces  the  e.m.f.  in- 
duced by  the  flux  L/Jco,  but  to  do  this  and  still  have  the  motor 
adapted  to  operate  at  the  same  voltage  and  speed,  it  is  necessary 
to  increase  the  number  of  armature  conductors  at  the  same 
time  that  the  flux  is  reduced.  Consequently,  while  the  in- 
ductance of  the  field  is  reduced,  that  of  the  armature  is  increased. 
Moreover,  on  account  of  the  strong  armature  reaction  and  the 
weak  field,  serious  distortion  of  the  flux  would  result,  and  the 
motor  would  spark  badly. 

294.  Compensating  Winding. — Fortunately,  however,  it  is 
possible  to  provide  a  winding  known  as  a  compensating  winding 
to  render  the  armature  nearly  non-inductive.  This  can  not  be 
done  in  the  case  of  the  field  as  the  field  flux  is  essential  to  the 
operation  of  the  machine.  The  flux  due  to  the  armature  on  the 
other  hand  may  be  regarded  as  a  stray  flux  which  is  not  es- 
sential to  operation,  and  which  in  the  present  case  is  detrimental 
on  account  of  the  induced  e.m.f.  generated.  Figure  218  shows 
the  arrangement  of  coils  and  slots  in  a  compensating  winding. 
If,  in  addition  to  the  armature  conductors,  an  equal  number  of 
conductors  could  be  provided  in  the  same  position  as  the  arma- 
ture conductors,  each  conductor  carrying  a  current  equal  and 
opposite  to  the  armature  current,  the  inductance  of  the  armature 
would  be  zero.  In  addition,  it  would  be  necessary  that  the  com- 
pensating winding  be  stationary  as  otherwise  it  would  generate 
an  e.m.f.  equal  and  opposite  to  that  of  the  armature.  The 
nearest  one  can  come  to  the  ideal  construction  is  to  place  the 
compensating  conductors  on  the  field  structure  as  near  to  the 
armature  as  is  practicable,  and  connect  them  in  series  with 
the  armature  and  the  field.  Moreover,  it  is  impracticable  to 
cover  all  of  the  armature  surface  as  a  certain  amount  of  room 
must  be  left  for  the  main  field  coils.  The  compensation  will 
therefore  not  be  perfect.  In  the  figure  the  different  coils  are 
marked,  and  the  construction  will  be  readily  understood.  The 
series  connection  gives  assurance  that  the  compensating  current 
will  at  all  times  be  equal  to  the  main  current.  Compensating 


SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR 


295 


windings  are  not  confined  to  alternating-current  machines,  but 
are  frequently  used  for  continuous-current  motors  and  generators. 
It  is  possible,  in  this  way,  to  build  a  continuous-current  machine 
much  lighter  than  would  otherwise  be  possible.  The  interpole 
construction  that  is  used  in  continuous-current  machines  may 
be  considered  a  special  case  of  the  foregoing  in  which  only  a  por- 
tion of  the  armature  surface  is  compensated,  or  rather  over- 
compensated. 

With  the  construction  above  indicated,  it  becomes  possible 
to  use  a  very  weak  field  and  a  correspondingly  strong  armature, 
i.e.,  one  having  many  turns  of  wire  on  it.  Both  the  vectors 


FIG.  218. 

Lflu  and  Lalu,  can  therefore  be  made  short,  compared  with  the 
induced  e.m.f.,  and  the  power  factor  consequently  large. 

295.  Variation  of  Power  Factor  with  the  Load. — In  practice  a 
motor  of  this  type  is  usually  operated  at  a  constant  potential. 
If  this  is  the  case,  the  length  of  the  line  E  of  Fig.  217  will  be 
constant.  We  may,  therefore,  draw  a  circle  of  radius  E  about  the 
point  0  as  a  center,  and  the  extremity  of  the  vector  E  will  always 
fall  upon  this  circle.  The  vector,  E,  will  be  more  nearly  parallel 
to  the  line  representing  the  current,  the  smaller  the  current. 
In  fact,  with  zero  current  the  two  would  become  parallel,  and 
the  power  factor  would  be  unity.  If,  therefore,  a  curve  of  current 
and  power  factor  be  plotted,  the  power  factor  will  start  from 
unity,  with  zero  current,  and  will  become  less  as  the  current  is 
increased.  The  condition  of  zero  current  at  full  voltage  is, 


296      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

however,  not  attainable  in  such  a  motor,  since  with  zero  field, 
it  would  be  necessary  for  the  armature  to  rotate  at  an  infinite 
speed  in  order  to  generate  the  required  back  e.m.f. 

The  other  characteristics  of  such  a  motor,  which  are  usually 
plotted  with  currents  as  abscissae  such  as  speed,  torque  (or 
tractive  effort,  if  the  motor  is  used  in  railway  work),  horse-power 
output,  temperature  rise,  etc.,  will  in  general,  resemble  those  of  a 
series- wound  direct-current  motor.  The  torque  will,  however,  be 
nearly  proportional  to  the  square  of  the  current  since  the  magnetic 
circuit  is  relatively  unsaturated,  and  the  flux  is  thus  nearly  pro- 
portional to  the  current.  The  speed  at  any  given  current  will 
be  less  than  that  of  the  same  motor  operating  on  direct  current, 
since  in  the  case  of  alternating-current  operation,  the  motor  has 
only  to  generate  the  back  e.m.f.  corresponding  to  Ea  while  in  the 
direct-current  machine,  the  back  e.m.f.  would  be  equal  to  E  minus 
the  drop  in  the  windings,  or  Ral,  plus  Rfl. 

296.  Operation  on  Direct  Current. — As  before  indicated,  a 
motor  of  this  type  will  operate  even  better  on  direct  current  than 
on  alternating.  In  the  matter  of  control,  there  are  advantages 
in  the  use  of  the  alternating  current.  It  has  been  pointed  out 
that  with  direct  current,  the  speed  will  be  higher  and  consequently 
the  output  greater  for  the  same  current.  The  efficiency  will 
be  better  also  since  the  hysteresis  and  eddy-current  loss  in  the 
iron  of  the  field  will  be  eliminated.  The  armature  iron  loss  will 
be  less  since  for  the  same  effective  current  the  flux  with  direct 
current  will  be  only  about  70.7  per  cent,  as  great  as  on  alternating. 
Moreover,  with  alternating  current  the  flux  at  any  point  of  the 
armature  goes  through  a  somewhat  complicated  cycle,  usually 
causing  an  increased  loss. 

Since  the  losses  are  greater  with  the  alternating  current,  the 
heating  will  be  more  than  with  direct  current,  or  looking  at  the 
matter  from  the  other  standpoint,  the  machine  may  be  rated 
higher  when  operated  on  direct  current.  As  has  been  pointed 
out,  in  order  to  get  a  good  power  factor,  it  is  necessary  to  con- 
struct a  motor  of  this  type  with  a  very  weak  field.  If  the  machine 
were  to  be  operated  on  direct  current,  it  would  be  possible  to 
work  with  a  far  stronger  field,  thus  increasing  the  torque  and 
consequently  the  power  of  the  motor  in  the  same  proportion. 

The  foregoing  will  be  sufficient  to  indicate  that  the  single-phase 
alternating-current  commutator  motor,  in  its  present  form,  is  in 
every  respect  inferior  to  a  similar  direct-current  motor.  It 


SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR  297 

should  not  be  taken  from  this  that  the  motor  is  to  be  condemned. 
The  motor  is  only  one  element  of  a  system,  and  it  may  readily 
happen  that  the  disadvantage  under  which  the  motor  itself 
operates  is  more  than  offset  by  advantages  elsewhere  in  the 
system. 

297.  Commutation. — The  problem  of  commutation  is  perhaps 
the  most  serious  one  with  which  the  designers  of  single-phase 
commutator  motors  have  had  to  deal.  Since  the  current  is 
alternating  it  is  necessary,  at  the  peak  of  the  wave,  to  commutate 
41  per  cent,  more  current  in  the  alternating-current  motor  than 
in  the  direct- current  machine.  This  is  further  increased  by  the 
fact  that  both  the  efficiency  and  the  power  factor  are  lower 
than  in  a  direct-current  motor.  This  is,  however,  not  the  worst 
phase  of  the  situation.  As  was  pointed  out  in  considering  the 
subject  of  direct-current  commutation  (see  page  296),  the  coil 
under  commutation  is  in  a  neutral  field,  that  is,  it  has  no  e.m.f. 
induced  in  it  due  to  the  rotation  of  the  armature.  This  is  also 
true  in  the  case  of  the  alternating  motor,  as  far  as  the  e.m.f. 
due  to  the  rotation,  is  concerned.  An  examination  of  Fig.  216 
'  will  show,  however,  that  the  coils  short-circuited  by  the  brushes 
and  in  the  position  to  develop  no  e.m.f.  due  to  their  rotation,  are 
in  the  best  position  to  have  induced  in  them  an  e.m.f.  due  to  the 
alternation  of  the  flux.  They  are,  therefore,  the  seat  of  an  e.m.f. 
which  is  short-circuited  through  the  brushes,  and  this  e.m.f.  is 
present  even  though  the  armature  is  at  rest.  In  fact,  it  is 
independent  of  the  rate  of  rotation,  and  is  dependent  only  upon 
the  frequency  of  the  supply  and  upon  the  flux  passing, through  the 
coil. 

In  practice,  every  endeavor  is  made  to  decrease  the  value  of 
the  e.m.f.  induced  under  the  short-circuited  brush.  The  number 
of  turns  per  coil  is  usually  reduced  to  one,  and  a  lap  winding 
adopted.  The  e.m.f.  is  then  that  due  to  one  coil  only.  The 
strength  of  the  poles  is  reduced  to  the  lowest  possible  value. 
This  would  be  done  in  any  event  in  order  to  improve  the  power 
factor.  Moreover,  by  increasing  the  number  of  poles,  the  flux 
per  pole  may  be  decreased.  On  this  account,  the  number  of 
poles  employed  in  these  motors  is  far  in  excess  of  that  common 
in  continuous-current  motors. 

Even  with  all  of  these  modifications,  the  e.m.f.  short-circuited 
under  the  brush  is  far  too  great  to  allow  satisfactory  commuta- 
tion, except  in  the  smallest  machines.  The  most  common 


298      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

method  of  reducing  the  short-circuit  current  is  the  use  of  resist- 
ance leads.  These  consist  of  strips  of  resistance  material  con- 
nected between  the  commutator  bars  and  the  winding.  The 
connection  is  shown  in  Fig.  219.  In  practice,  the  leads  are 
frequently  doubled  and  laid  in  the  bottom  of  the  slots.  The 
current  from  the  brushes  passes  through  only  those  leads  which 
are  connected  to  the  commutator  bars  actually  in  contact  with 
the  brushes  at  any  given  instant.  Hence,  these  leads  need  not 
be  so  heavy  as  would  be  necessary  if  the  current  were  passing 
through  them  all  the  time.  Care  must,  however,  be  taken  that 
they  are  not  so  light  that  they  will  be  liable  to  be  burned  out  in 
case  the  motor  should  fail  to  start  at  once  when  the  current  is 
applied.  Under  these  circumstances,  the  current  will  be  confined 
to  a  few  leads,  and  these  will,  of  course,  become  hotter  than 
normal. 


Armature 
Winding 


Resistance 
Leads 

Commutator 

FIG.  219. 

The  difficulty  due  to  the  generation  of  an  e.m.f.  in  the  coils 
undergoing  commutation,  can  be  decreased  by  the  use  of  a 
lower  frequency.  This  results  in  an  improvement  of  the  power 
factor,  since  the  vectors  L0/co  and  L//CO,  in  Fig.  217  are  propor- 
tional to  the  frequency.  On  the  other  hand,  advantage  may  be 
taken  of  these  facts  to  increase  the  strength  of  the  magnetic 
field  employed,  and  thus  increase  the  rating  of  the  motor.  This 
undoubted  advantage  of  the  lower  frequency  motor  has  led  to  the 
serious  proposal  to  standardize  another  frequency  for  railway 
work.  The  frequency  most  frequently  mentioned  in  this  con- 
nection is  15  cycles.  This  would  result  in  an  increase  in  the 
weight  and  a  decrease  in  the  efficiency  of  the  generators  and 
transformers.  Moreover,  this  frequency  is  not  well  adapted 
to  the  operation  of  small  and  medium-sized  induction  motors. 

298.  Control  of  Single-phase  Motors. — When  continuous- 
current  motors  are  used  on  electric  cars  or  locomotives,  the  con- 


SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR  299 

trol  of  the  car  is  accomplished  by  means  of  resistors  in  connection 
with  different  arrangements  of  the  motors.  In  the  case  of  the 
alternating-current  commutator  motors,  a  more  efficient  and 
perhaps  simpler  method  is  used.  The  current  is  always  supplied 
to  the  car  or  locomotive  at  a  high  voltage,  varying  usually  from 
4400  volts  to  11,000  volts.  This  necessitates  the  employment 
of  a  transformer  on  the  car  to  reduce  the  voltage  to  that  suitable 
for  use  on  the  motors.  It  is  a  comparatively  easy  matter  to 
provide  this  transformer  with  a  number  of  taps  so  that  any 
suitable  voltage  can  be  impressed  on  the  motor  terminals.  The 
necessity  for  using  resistors  is  removed.  Thus  the  loss  due  to 
the  use  of  resistance  is  avoided  and  the  efficiency  is  improved. 
This  will  be  especially  important  if  frequent  stops  and  starts 
are  to  be  made,  or  if  a  great  deal  of  slow-speed  running  is 
necessary. 

Another  advantage  of  this  method  of  control  is  that  it  gives 
a  method  of  making  up  time  in  emergencies.  It  is  merely  nec- 
essary to  provide  an  extra  high-voltage  tap  to  be  used  only  in 
case  a  speed  above  normal  is  necessary.  This  may  also  be 
useful  in  case  of  low  voltage  on  the  line. 

As  has  been  pointed  out,  motors  of  this  type  are  capable  of 
operation  on  continuous-current  circuits,  in  fact,  their  operation 
is  better  on  the  latter  than  on  alternating  current.  This  is  a 
very  valuable  property,  particularly  in  the  case  of  cars  used  in 
interurban  service.  Such  cars  almost  invariably  use  the  tracks 
of  city  cars,  and  these  are  always  operated  by  continuous  cur- 
rent. If  the  motors  of  the  interurban  cars  were  incapable  of 
operation  on  direct  current,  it  would  be  necessary  to  transfer 
passengers,  or  provide  special  locomotives  to  haul  the  inter- 
urban cars  through  the  city.  The  same  situation  sometimes 
arises  even  in  the  case  of  trunk-line  electrifications.  The  control 
apparatus  used  on  continuous-current  cars  can  be  used  with  al- 
ternating-current motors.  The  reverse  is,  however,  not  true. 
It  is  therefore  customary  to  sacrifice  the  advantage  in  point 
of  efficiency  that  the  alternating-current  control  possesses 
rather  than  go  to  the  complication  of  two  sets  of  control 
apparatus. 

The  voltage  used  on  single-phase  commutator  motors  is  about 
200  volts.  This  is  undesirably  low  compared  with  direct-current 
practice,  as  it  necessitates  a  commutator  about  twice  as  large 
as  would  be  required  for  the  same  power  at  550  volts.  This 


300      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

low  voltage  is,  however,  a  necessity  on  account  of  the  fact 
previously  mentioned  that  the  armature  coils  are  usually  wound 
with  only  one  turn  per  coil  in  order  to  reduce  the  difficulty  of 
commutation.  This  in  turn  involves  the  use  of  one  commu- 
tator bar  per  coil,  and  consequently  the  number  of  bars  is  great. 
It  is  impracticable  to  crowd  more  than  a  limited  number  of 
bars  within  the  limit  of  size  of  the  commutator.  Hence  the 
voltage  must  be  kept  low. 

299.  Other  Types  of  Single-phase  Commutator  Motors. — 
In  addition  to  the  series  type  of  motor  just  described,  numerous 
modifications  have  been  introduced.  In  general,  it  may  be 
said  that  these  modified  forms  depend  upon  induction  to  pro- 
duce the  current  in  one  or  more  of  the  elements,  instead  of  em- 
ploying conduction  as  in  the  series  motor.  When  this  is  the 


FIG.  220. 

case,  they  are  obviously  incapable  of  operation  on  continuous 
current. 

Figure  220  shows  in  a  diagrammatic  form  the  connection 
of  the  three  elements  of  a  single-phase  series  motor.  The  coil 
marked  F  is  the  field  coil,  C  is  the  compensating  coil,  and  A  is 
the  armature.  The  latter,  for  the  purposes  of  the  diagram, 
is  supposed  to  be  so  wound  that  its  "poles"  are  opposite  the 
brushes.  The  simplest  modification  of  these  connections  is 
illustrated  in  Fig.  221,  in  which  the  compensating  coil,  instead 
of  being  connected  in  series,  is  short-circuited  on  itself.  It  will 
then  act  like  the  short-circuited  secondary  of  a  transformer,  of 
which  the  armature  is  the  primary.  Such  a  current  will  flow 
that  the  ampere  turns  of  the  coil  will  be  approximately  equal  to 
the  ampere  turns  of  the  armature.  The  coil  may  be  wound  with 
any  convenient  size  of  wire  and  number  of  turns,  sufficient  cop- 
per being  provided  to  carry  the  current  required.  The  opera- 


SINGLE-PHASE  COMMUTATOR  TYPE  MOTOR 


301 


tion  on  alternating  current  will  not  be  markedly  different 
from  that  of  the  series  motor.  On  continuous  current,  no 
current  would  flow  in  the  compensating  coil,  and  on  account 
of  the  great  strength  of  the  armature  compared  with  the  field, 
there  would  be  such  serious  sparking  that  operation  would 
be  impracticable. 


FIG.  221. 

300.  Repulsion  Motor. — The  motor  illustrated  in  Fig.  222  is 
known  as  the  repulsion  motor.  The  armature  is  not  connected 
in  series  with  the  main  circuit,  but  is  short-circuited  and  re- 
ceives its  current  by  induction.  One  very  important  advantage 
of  this  method  of  connection  is  that  the  field  and  compensating 


FIG.  222. 

coil  may  be  wound  for  high  voltage,  while  the  armature  is  wound 
for  whatever  voltage  is  most  suitable  for  the  design  in  hand. 
With  this  type  of  motor  the  use  of  a  transformer  on  the  car  can, 
therefore,  in  many  instances  be  avoided.  This  method  of  con- 
nection, however,  leads  to  quite  radical  changes  in  the  char- 
acteristics of  the  motor,  particularly  as  regards  commutation. 


302      PRINCIPLES  OF  DYNAMO  ELECTRIC  MACHINERY 

Nevertheless,  the  series  characteristic  is  retained.  In  practice, 
repulsion  motors  are  usually  wound  with  a  distributed  winding 
for  both  the  compensating  coil  and  the  field  coil.  With  this 
carried  to  the  limit,  it  will  be  apparent  that  the  two  coils  become 
really  one,  with  the  axis  of  the  brushes  displaced  from  the  axis 
of  the  coil. 


INDEX 

(Numbers  refer  to  articles) 
A 

Acyclic  machines,  31 

Adjustable  speed  motors,  see  Speed. 

Air  gap  clearance,  282 

Alternating  currents,  definition,  108 

effective  values  of  current  and  voltage,  118 

frequency,  110 

methods  of  treating  a.-c.  waves,  112 
analytical  method,  113 
vector  method,  114 

phase  difference,  115 

power  factor,  136 

sine  curve,  111 

vector  addition,  117 

wave  shape,  109 
Alternators,  153 

magnetic  field,  163 

power,  161,  168,  169,  171 
factor,  172 

single  phase,  158,  162,  164 

three  phase,  157,  158,  159,  162,  166 

two  phase,  154,  155,  156,  165 

voltage  current  relations,  160 
Ammeter,  90 
Ampere,  10 
Apparatus,  circuit  breakers,  71 

field  discharge  switch,  124 

no  voltage  release,  69 

protective,  70 

starting  rheostats,  67,  68,  261-265,  274 
Applications  of  d.-c.  machines,  104,  105,  106 
Armature,  action,  21 

construction,  26 

definition,  19 

loss,  72 

reaction,  41,  42,  219,  251,  254 

resistance,  100 

windings,  26,  27,  28,  153,  154,  157 
Auto  starters,  262 

B 

Back  e.m.f.,  35 

303 


304  INDEX 

Brake  test,  80 

Brushes,  effect  of  rocking,  77 


Capacitance,  140 

of  transmission  lines,  139 
Cascade  connection,  268 

converter,  243 
Characteristic  curve  of  compound-wound  generator,  49 

separately  excited  generator,  46 

series-wound  generator,  48 

shunt-wound  generator,  47 
Circle  diagram,  260 
Circuit  breaker,  71 
Commutating  machines,  31,  226,  275,  286,  300 

poles,  78,  98 

Commutation,  76,  235,  297 
Commutator,  22,  33 

type  of  induction  motor,  287 
Compensating  winding,  294 
Compensator,  262 
Compound  generator,  49 

motor,  40 

cumulative,  61 
differential,  62 
Concatenation,  268 
Condenser,  137,  138 

synchronous,  209,  224 
Connections  of  rotary,  237 
Constant  current  system,  43 
transformer,  185 

potential  system,  44 
Cooling  of  transformer,  187 
Coulomb,  137 
Current,  in  line,  142,  143 

rotor,  249,  250 

sheet,  32 

space  curve,  199 

D 

D'Arsonval  type  instrument,  91 
Damping  grids,  213 
Delta  connections,  159 
Demagnetization,  42 
Differential  compounding,  62 
Distorted  waves,  210 
Distribution,  43,  44,  45 
Double  Y-connection  for  rotaries,  237 


Drum  winding,  26 
Dynamo,  31 
Dyne,  6 


INDEX  305 


E 


Eddy  currents  in  transformer,  180 
Effect  of  voltage  on  amount  of  copper  required,  54 
Effective  values  of  current  and  e.m.f.,  118 
Efficiency,  74,  79,  86,  89 

of  generator,  88 

of  induction  motor,  276 

of  motor,  86 

of  rotary  converter  vs.  motor  generator,  238 

of  synchronous  motor,  276 

of  transformer,  189 

with  speed,  89 
Electrodynamometer,  147 
Electromotive  force,  9,  35,  36 
Electrostatic  voltmeter,  151 
Equalizer,  53 


Farad,  137 

Field  current,  206 

discharge  switch,  124 

excitation,  37 

winding,  20,  227 
Flux,  7,  15 

curves,  199 

leakage,  183 

sheet,  32 
Frequency,  110,  236,  238,  240 

.  changers,  268,  269 
Fuses,  70 


Generation  of  electromotive  force,  9,  35,  36 
Generators,  alternating  current,  153 

compound,  49 

efficiency,  88 

heating,  73 

induction,  256 

parallel  operation,  51,  52,  53,  204 

regulation',  50,  see  Regulation. 

separately  excited,  37,  46 

series,  48 

shunt,  47 

speed  of,  72 
20 


306  INDEX 

H 

Heating  of  generators,  73 

of  motors,  73 

of  rotaries,  234 

single-phase  motors,  288 

transformers,  188 

Hot  wire  measuring  instruments,  149 
Hunting  of  synchronous  motors,  211,  212,  280 
Hysteresis  in  transformer,  180 

I 

Impedance,  143 

Inductance,  119,  120,  121,  125,  128,  131,  140 
Induction  generator,  256 
motor,  31,  243 

adjustable  speed,  266 

air  gap-clearance,  282 

attention  required,  283 

auto-starter,  262 

circle  diagram,  260 

efficiency,  276 

magnetic  field  (rotating),  248,  272 

overload  capacity,  279 

power  factor,  277 

production  of  current  in  rotor,  249 

pulling  out  point,  254 

rotor,  see  Rotor. 

single  phase,  271,  285,  see  Single  phase. 

slip,  254 

speed,  278,  284,  255 

cascade  connection,  268 

changing  number  of  poles,  267 

commutator  type,  269 

concatenation,  268 

regulation,  278 

slow,  284 

wound  rotor,  270 
squirrel  cage,  247,  252,  261 
starters,  auto-starter  or  compensator,  262 

resistance,  263,  265 

split  phase,  274 

star-delta,  264 

switch,  261 

wound  rotor,  265 
starting  torque,  252,  273,  281 
stator,  246 
torque,  251 


INDEX  307 


Induction  motor,  vector  diagrams,  257,  258,  259 

wound  rotor,  253 
Inductor,  20 
Instruments,  see  Meters. 
Interpoles,  78 


Lap  winding,  27 
Leakage,  flux,  183 
Line,  capacitance,  139 

regulation,  173-176 
Lines  of  force,  7 

induction,  9 
Load,  method  of  connecting,  156 

three  phase,  157,  159 

two  phase,  156 
Losses,  armature  copper,  85 

in  direct  current  machines,  82 

in  shunt  field,  84 

in  transformer,  180 

stray  power,  83 


M 


Magnetic  circuit,  15,  99 

field,  7,  10 

(rotating),  163,  248,  272 
Magnetism,  67 
Magnetization  curves,  17 
Magnetizing  effect,  41 
Magneto-motive  force,  14 
Mathematical  treatment,  capacitance,  142 

power,  134 

Measuring  instruments,  see  Meters. 
Mechanical  analogy,  122,  123,  126 
Mercury  arc  rectifier,  244 
Mesh  connection,  159 
Meters,  ammeter,  90 

D'Arsonval  type,  91 

electrodynamometer  type,  147 

electrostatic  voltmeter,  151 

hot-wire  instruments,  149 

instrument  transformers.  186 

oscillograph,  152 

plunger  type,  93 

polyphase  wattmeters,  171 

spark  gap,  150 

voltmeter,  90,  92 

watt-hour  meter,  95 


308  INDEX 

Meters,  wattmeter,  94,  148,  168,  169,  170 
Microfarad,  137 
Motors,  acyclic,  31 

adjustable  "speed,  96 

characteristics,  56 

commutating,  31 

compound,  40,  61,  62,  65 

differential  compound,  62 

efficiency,  86 

elementary  form,  18,  21,  23,  30 

equation,  58 

heating,  73 

induction,  see  Induction  motors. 

operation,  57 

rectifying,  31 

repulsion,  275,  300 

rotation,  66 

series,  39,  60,  64 

shunt,  38,  59,  63,  64 

field  control,  97 

single  phase,  see  Single-phase  motors. 
speed,  72 
control,  96 

change  of  magnetic  circuit,  99 
multivoltage  system,  102 
resistance  in  armature  circuit,  100 
resistance  in  shunt  field,  97 
two  commutators,  101 
Ward -Leonard  system,  103 
synchronous,  see  Synchronous  motors. 
unipolar,  31 

Multipolar  machines,  25 
Multivoltage  system  (speed),  102 

N 
No-voltage  release,  69 

O 

Ohm's  law,  2 

Operating  of  electric  machine,  226,  285,  296 

of  rotary  converter,  226 

with  distorted  waves,  210 
Oscillatory  discharges,  145 
Oscillograph,  152 
Overcompounding,  61 
Overload  capacity,  induction  motor,  279 
synchronous  motor,  279 


INDEX  309 


Parallel  operation  of  generators,  51 
of  compound  machines,  53 
of  shunt  machines,  52 
of  synchronous  machines,  204 

Parallel  winding,  27 

Permeability,  8,  16 

Phase  difference,  115 

Polyphase  potential  regulator,  232 

Power,  11,  94,  129,  133,  135,  161,  168,  169,  170,  171 

Power  factor,  136 

effect  on  torque,  201 

of  induction  motor,  277,  279 

of  single-phase  motors,  289,  293,  295 

of  synchronous  motor,  172,  201,  202,  277 

Prime  mover,  effect  of  regulation,  207 

Protective  apparatus,  70 

Pull-out  point,  254 

Q 

Quantity  of  electricity,  137 

R 

Rating,  221 

Reactance,  143 

Reaction,  armature,  41,  42,  219,  251,  254 

Regulation,  220,  222,  223 

line,  173,  174,  175,  176 

method  of  testing,  50 

motor  generator  vs.  rotary  converter,  238 

of  generators,  45,  46,  50 
compound,  49 
separately  excited,  46 
series,  48 
shunt,  47 

of  induction  motors,  278,  284 

of  prime  mover,  207 

of  rotary  converter,  242 

of  synchronous  motor,  see  Syn.  mot. 

speed,  278,  284 

transformer,  184 

voltage,  220,  222,  223 

Regulators,  voltage  for  rotary  converters,  238 
Reluctance,  15 
Repulsion  motor,  275,  300 
Residual  magnetism,  17 
Resistance,  3,  4,  76,  125,  127,  131,  140,  143,  252 

change  with  temperature,  3 


310  INDEX 

Resistance  definition,  3 

in  series  and  parallel,  4 
Resistance  leads,  263 
starter,  263,  265 
Resonance,  144 
Reversed  polarity,  230 
Rheostat,  starting,  67,  68 
Rocking  brushes,  77 
Rotary  converter,  cascade,  243 
costs,  239 
commutation,  235 
connections,  237 
double  Y-connection,  237 
efficiency,  241 
field  winding,  227 
frequency,  236,  240 
heating,  234 
operation,  226 
regulation,  242 

reversed  polarity  at  start,  230 
six-phase  connection,  237 
split  pole,  233 
starting,  229 
voltage  control,  231,  233 
regulators,  232 
relations,  228,  242 
vs.  motor  generator,  238 
Rotation  of  machines,  66 
Rotor,  247 

current,  249,  250 

reaction,  251,  254 

resistance,  252 

rotating  magnetic  field,  248,  272 

squirrel  cage,  247,  252,  261 

wound,  247,  253 


Separately  excited  generator,  37,  46 
Series  field,  20 

generator,  48 

system  (distribution),  43 

wound  machine,  18,  39 
Shell  type  transformer,  187 
Shunt  field,  97 

generator,  47 

wound  machines,  38 
Sine  curve,  111 
Single-phase  commutator  motor,  285,  286,  299 


INDEX  311 


Single-phase  type,  series-wound  induction  motor,  286,  287 
commutation,  297 
compensating  winding,  294 
control,  298 

direct-current  operation,  296 
generated  electromotive  force,  290 
heating,  288 

induced  electromotive  force,  291 
operation,  285,  286,  296,  298 
power  factor,  289,  293,  295 
vector  diagram,  292 
voltage,  290,  291 
generator,  153 
induction  motor,  271 

rotating  magnetic  field,  272 
split-phase  starters,  274 
starting  as  repulsion  motor,  275 

torque,  273 
system,  153,  164,  286 

Six-phase  rotary  converter  connection,  237 
Slip,  254 
Solenoid,  12,  13 
Space  curve  of  current,  199 

of  electromotive  force,  198 
of  flux,  199 

Spark-gap  voltmeter,  150 
Sparking,  75 
Speed,  72 

changing  magnetic  circuit,  99 
commutating  poles,  98 
direct-current  motor,  72 
generator,  72 

induction  motor,  see  Induction  motor. 
multi-voltage  system,  102 
regulation,  278 

resistance  in  armature  circuit,  100 
shunt-field  control,  97 

synchronous  motors,  278,  see  Synchronous  motors. 
two  commutators,  101 
Ward  Leonard  system,  103 
Speed  torque  curves,  compound  motors,  61 
differential  compound  motors,  62 
induction  motors,  270 
series  motors,  60 
shunt  motors,  59 
Split-phase  starter,  274 

pole  rotories,  233 
Squirrel  cage,  247,  252,  261 


312  INDEX 

Star  connection,  159 
Star-delta  starter,  264 

Starters  for  induction  motors,  261-265,  274 
Starting  rheostats,  67,  68 
rotary  converters,  229 
synchronous  motors,  215 
Starting  induction  motors,  see  Induction  motors. 

torque,  polyphase  induction  motor,  252,  273,  281 
single-phase  induction  motor,  273 
synchronous  motor,  281,  see  Synchronous  motor. 
Stator,  246 
Stray  power  loss,  81 
Synchronizing  by  lamps,  215 
Synchronous  condenser,  209,  224 
converter,  225 

generator  and  motor,  31,  167,  196,  214 
air-gap  clearance,  282 
armature  reaction,  219 
construction,  196 
curves,  198,  199 

effect  of  charging  field  current,  206 
efficiency,  276 
hunting,  211,  212,  213,  280 
operation  with  distorted  waves,  210 
overload  capacity,  279 
parallel  operation,  204 
power,  168,  169,  170 
factor,  172,  177 

on  torque,  201,  202 
rating,  221 

regulation,  line,  173,  174,  175,  176 
prime  mover,  207 
speed,  278,  284 
voltage,  220,  222,  223 
starting,  215,  216,  217,  218 
synchronizing,  215,  216 
two  wattmeter  method,  170 
vector  diagrams,  208 
voltage  and  current  relations,  205 
Synchroscope,  216 


Temperature,  variation  of  resistance,  3 
Three-phase  generator,  166 
Three-wire  system,  55 
Time  curves  current,  109,  110 
voltage,  110 


INDEX  313 


Torque,  induction  motor,  251,  295 
series  motor,  64 
shunt  motor,  64 
synchronous  motor,  200 
Transformer,  177,  178,  179 

connections,  open  delta,  194 

single-phase,  190 

three-phase,  192,  193 

two-phase,  191 
constant  current,  185 
cooling,  188 
core  loss,  180 

type,  178,  187 
cruciform  type,  187 
eddy  currents,  180 
efficiency,  189 
hysteresis,  180 
instrument  transformer,  186 
leakage  flux,  183 
losses,  189 
regulation,  184 
shell  type,  187 

transformation  of  number  of  phase,  195 
under  load,  182 
vector  diagram,  181,  182 
Two-phase  generator,  165 
Two-wattmeter  method,  170 


U 


Unipolar  machines,  31 
Units  of  capacity,  137 

of  current,  10 

of  electromotive  force,  2 

of  quantity,  137 


Variable  speed  motors,  266-270 
Vector  diagrams,  alternator,  208 

induction  motor,  257,  258,  259 
single-phase  commutator  motor,  292 
transformer,  181,  182 
method,  114,  117,  132,  141 
Volt,  2 

Voltage  and  current  relations  of  synchronous  machine,  205,  220 
control,  231 
curves,  198 
generated,  290 


314  INDEX 

Voltage  induced,  291 

regulation,  231,  184 

regulators,  232 

relation,  228 
Voltmeter,  90,  92 


W 


Ward -Leonard  system,  88 
Wattmeter,  94,  148,  168,  169,  170 
Wave  distorted,  210 

shape,  109 

winding,  28,  29 
Winding,  armature,  26 

drum,  26 

lap,  27 

series,  28,  29 

single-phase,  153 

three-phase,  157 

two-phase,  154 

wave,  28,  29 
Wire  table,  5 
Work,  11,  95 
Wound  rotor,  253 

for  adjustable  speed,  270 

starter,  265 


Y-connection,  159 


YC  40385 


3°^  . 


3cc°o  _ 

$$(i 


\ 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


_ 


' 


